Package 'distrMod'

Description

Based on the packages distr and distrEx package distrMod provides a flexible framework which allows computation of estimators like maximum likelihood or minimum distance estimators for probability models.

Details

Classes

[*]: there is a generating function with the same name
##########################
ProbFamily classes
##########################
slots: [<name>(<class>)]
name(character), distribution(Distribution),
distrSym(DistributionSymmetry), props(character)
"ProbFamily"
|>"ParamFamily"     [*]
additional slots:
param(ParamFamParameter), modifyParam(function),
startPar(function), makeOKPar(function), fam.call(call)
|>|>"L2ParamFamily" [*]
additional slots:
L2deriv(EuclRandVarList), L2deriv.fct(function),
L2derivSymm(FunSymmList), L2derivDistr(DistrList),
L2derivDistrSymm(DistrSymmList), FisherInfo(PosSemDefSymmMatrix),
FisherInfo.fct(function)
|>|>|>"BinomFamily" [*]
|>|>|>"PoisFamily"  [*]
|>|>|>"BetaFamily"  [*]
|>|>|>"NbinomFamily" [*]
|>|>|>"NbinomwithSizeFamily" [*]
|>|>|>"NbinomMeanSizeFamily" [*]
|>|>|>"L2GroupParamFamily"
additional slots:
LogDeriv(function)
|>|>|>|>"L2ScaleShapeUnion"  /VIRTUAL/
|>|>|>|>|>"GammaFamily" [*]
|>|>|>|>"L2LocationScaleUnion"  /VIRTUAL/
additional slots:
locscalename(character)
|>|>|>|>|>"L2LocationFamily"              [*]
|>|>|>|>|>|>"NormLocationFamily"          [*]
|>|>|>|>|>"L2ScaleFamily"                 [*]
|>|>|>|>|>|>"NormScaleFamily"             [*]
|>|>|>|>|>|>"ExpScaleFamily"              [*]
|>|>|>|>|>|>"LnormScaleFamily"            [*]
|>|>|>|>|>"L2LocationScaleFamily"         [*]
|>|>|>|>|>|>"NormLocationScaleFamily"     [*]
|>|>|>|>|>|>"CauchyLocationScaleFamily"   [*]
|>|>|>|>|>|>"LogisticLocationScaleFamily" [*]
and a (virtual) class union "L2ScaleUnion"  between
   "L2LocationScaleUnion"  and "L2ScaleShapeUnion"
##########################
ParamFamParameter
##########################
"ParamFamParameter" [*] is subclass of class "Parameter" of package "distr".
Additional slots:
main(numeric), nuisance(OptionalNumeric), fixed(OptionalNumeric),
trafo(MatrixorFunction)
##########################
Class unions
##########################
"MatrixorFunction" = union("matrix", "OptionalFunction")
"PrintDetails" = union("Estimate", "Confint",
                   "PosSemDefSymmMatrix",
                   "ParamFamParameter", "ParamFamily")
##########################
Symmetry classes            (other classes moved to package "distr")
##########################
slots:
type(character), SymmCenter(ANY)
"Symmetry"   (from package "distr")
|>"FunctionSymmetry"
|>|>"NonSymmetric"      [*]
|>|>"EvenSymmetric"     [*]
|>|>"OddSymmetric"      [*]
list thereof
"FunSymmList"           [*]
##########################
Matrix classes              (moved to package "distr")
##########################
slots:
none
"PosSemDefSymmMatrix" [*] is subclass of class "matrix" of package "base".
|>"PosDefSymmMatrix"  [*]
##########################
Norm Classes
##########################
slots:
name(character), fct(function)
"NormType"        [*]
|>"QFNorm"        [*]
Additional slots:
QuadForm(PosSemDefSymmMatrix)
|>|>"InfoNorm"    [*]
|>|>"SelfNorm"    [*]
##########################
Bias Classes
##########################
slots:
name(character)
"BiasType"
|>"symmetricBias"   [*]
|>"onesidedBias"
Additional slots:
sign(numeric)
|>"asymmetricBias"  [*]
Additional slots:
nu(numeric)
##########################
Risk Classes
##########################
slots:
type(character)
"RiskType"
|>"asRisk"
|>|>"asCov"       [*]
|>|>"trAsCov"     [*]
|>"fiRisk"
|>|>"fiCov"       [*]
|>|>"trfiCov"     [*]
|>|>"fiHampel"    [*]
Additional slots:
bound(numeric)
|>|>"fiMSE"       [*]
|>|>"fiBias"      [*]
|>|>"fiUnOvShoot" [*]
Additional slots:
width(numeric)
Risk with Bias:
"asRiskwithBias"
slots: biastype(BiasType), normtype(NormType),
|>"asHampel"      [*]
Additional slots:
bound(numeric)
|>"asBias"        [*]
|>"asGRisk"
|>|>"asMSE"       [*]
|>|>"asUnOvShoot" [*]
Additional slots:
width(numeric)
|>|>"asSemivar"   [*]
##########################
Estimate Classes
##########################
slots:
name(character), estimate(ANY),
samplesize(numeric), asvar(OptionalMatrix),
Infos(matrix), nuis.idx(OptionalNumeric)
fixed.estimate(OptionalNumeric),
estimate.call(call), trafo(list[of function, matrix]),
untransformed.estimate(ANY),
untransformed.asvar(OptionalMatrix)
criterion.fct(function), method(character),
"Estimate"
|>"MCEstimate",
Additional slots:
criterion(numeric)
##########################
Confidence interval class
##########################
slots:
type(character), confint(array),
estimate.call(call), name.estimate(character),
trafo.estimate(list[of function, matrix]),
nuisance.estimate(OptionalNumeric)
"Confint"

Methods

besides accessor and replacement functions, we have methods solve, sqrt for matrices checkL2deriv, existsPIC for class L2ParamFamily LogDeriv for class L2GroupParamFamily validParameter for classes ParamFamily, L2ScaleFamily, L2LocationFamily, and L2LocationScaleFamily modifyModel for the pairs of classes L2ParamFamily and ParamFamParameter, L2LocationFamily and ParamFamParameter, L2ScaleFamily and ParamFamParameter, L2LocationScaleFamily and ParamFamParameter, GammaFamily and ParamFamParameter, and ExpScaleFamily and ParamFamParameter mceCalc for the pair of classes numeric and ParamFamily mleCalc for the pairs of classes numeric and ParamFamily, numeric and BinomFamily, numeric and PoisFamily, numeric and NormLocationFamily, numeric and NormScaleFamily, and numeric and NormLocationScaleFamily coerce from class MCEstimate to class mle confint for class Estimate profile for class MCEstimate

Functions

Management of global options:
"distrModOptions", "distrModoptions", "getdistrModOption",
check for ker of matrix: "isKerAinKerB"
particular norms: "EuclideanNorm", "QuadFormNorm"
onesided bias: "positiveBias", "negativeBias",
Estimators:
"Estimator", "MCEstimator", "MLEstimator", "MDEstimator"
special location/scale models:
"L2LocationUnknownScaleFamily", "L2ScaleUnknownLocationFamily"
some special normal models:
"NormScaleUnknownLocationFamily", "NormLocationUnknownScaleFamily",

Start-up-Banner

You may suppress the start-up banner/message completely by setting options("StartupBanner"="off") somewhere before loading this package by library or require in your R-code / R-session. If option "StartupBanner" is not defined (default) or setting options("StartupBanner"=NULL) or options("StartupBanner"="complete") the complete start-up banner is displayed. For any other value of option "StartupBanner" (i.e., not in c(NULL,"off","complete")) only the version information is displayed. The same can be achieved by wrapping the library or require call into either suppressStartupMessages() or onlytypeStartupMessages(.,atypes="version"). As for general packageStartupMessage's, you may also suppress all the start-up banner by wrapping the library or require call into suppressPackageStartupMessages() from startupmsg-version 0.5 on.

Demos

Demos are available — see demo(package="distrMod").

Scripts

Example scripts are available — see folder ‘scripts’ in the package folder to package distrMod in your library.

Package versions

Note: The first two numbers of package versions do not necessarily reflect package-individual development, but rather are chosen for the distrXXX family as a whole in order to ease updating "depends" information.

Note

Some functions of packages stats, base have intentionally been masked, but completely retain their functionality — see distrModMASK(). If any of the packages stats4, fBasics is to be used together with distrMod, the latter must be attached after any of the first mentioned. Otherwise confint() defined as method in distrMod may get masked.
To re-mask, you may use confint <- distrMod::confint. See also distrModMASK()

Author(s)

Peter Ruckdeschel [email protected],
Matthias Kohl [email protected]
Maintainer: Peter Ruckdeschel [email protected]

References

M. Kohl and P. Ruckdeschel (2010): R Package distrMod: S4 Classes and Methods for Probability Models. Journal of Statistical Software, 35(10), 1-27. doi:10.18637/jss.v035.i10 (see also vignette("distrMod")) P. Ruckdeschel, M. Kohl, T. Stabla, F. Camphausen (2006): S4 Classes for Distributions, R News, 6(2), 2-6. https://CRAN.R-project.org/doc/Rnews/Rnews_2006-2.pdf A vignette for packages distr, distrSim, distrTEst, and distrEx is included into the mere documentation package distrDoc and may be called by require("distrDoc");vignette("distr")

Description

.checkEstClassForParamFamily-methods

Usage

.checkEstClassForParamFamily(PFam, estimator)
## S4 method for signature 'ANY,ANY'
.checkEstClassForParamFamily(PFam, estimator)

Arguments

Details

The respective methods can be used to cast an estimator to a model-specific subclass with particular methods.

Value

The (default) ANY,ANY-method returns the estimator unchanged.

Author(s)

Peter Ruckdeschel [email protected]

Description

Adds alpha transparency to a given color.

Usage

addAlphTrsp2col(col, alpha=255)

Arguments

Value

a color in rgb coordinates

Author(s)

Peter Ruckdeschel [email protected]

Examples

## IGNORE_RDIFF_BEGIN
  addAlphTrsp2col(rgb(1,0.3,0.03), 25)
  ## gives "#FF4C0819" on 32bit and "#FF4D0819" on 64bit
## IGNORE_RDIFF_END
  addAlphTrsp2col("darkblue", 25)
  addAlphTrsp2col("#AAAAAAAA",25)
  palette(rainbow(6))
  addAlphTrsp2col(2, 25)

Description

Generates an object of class "asBias".

Usage

asBias(biastype = symmetricBias(), normtype = NormType())

Arguments

Value

Object of class "asBias"

Author(s)

Matthias Kohl [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

asBias-class

Examples

asBias()

## The function is currently defined as
function(biastype = symmetricBias(), normtype = NormType()){ 
     new("asBias",biastype = biastype, normtype = normtype) }

Description

Class of standardized asymptotic bias; i.e., the neighborhood radius is omitted respectively, set to $1$.

Objects from the Class

Objects can be created by calls of the form new("asBias", ...). More frequently they are created via the generating function asBias.

Slots

type

Object of class "character": “asymptotic bias”.

biastype

Object of class "BiasType": symmetric, one-sided or asymmetric

normtype

Object of class "NormType": norm in which a multivariate parameter is considered

Extends

Class "asRiskwithBias", directly.
Class "asRisk", by class "asRiskwithBias"
Class "RiskType", by class "asRisk".

Author(s)

Matthias Kohl [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

asRisk-class, asBias

Examples

new("asBias")

Description

Generates an object of class "asCov".

Usage

asCov()

Value

Object of class "asCov"

Author(s)

Matthias Kohl [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

asCov-class

Examples

asCov()

## The function is currently defined as
function(){ new("asCov") }

Description

Class of asymptotic covariance.

Objects from the Class

Objects can be created by calls of the form new("asCov", ...). More frequently they are created via the generating function asCov.

Slots

type

Object of class "character": “asymptotic covariance”.

Extends

Class "asRisk", directly.
Class "RiskType", by class "asRisk".

Methods

No methods defined with class "asCov" in the signature.

Author(s)

Matthias Kohl [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

asRisk-class, asCov

Examples

new("asCov")

Description

Class of special convex asymptotic risks.

Objects from the Class

A virtual Class: No objects may be created from it.

Slots

type

Object of class "character".

biastype

Object of class "BiasType": symmetric, one-sided or asymmetric

normtype

Object of class "NormType": norm in which a multivariate parameter is considered

Extends

Class "asRisk", directly.
Class "RiskType", by class "asRisk".

Methods

No methods defined with class "asGRisk" in the signature.

Author(s)

Matthias Kohl [email protected]

References

Ruckdeschel, P. and Rieder, H. (2004) Optimal Influence Curves for General Loss Functions. Statistics & Decisions 22, 201-223.

See Also

asRisk-class

Description

Generates an object of class "asHampel".

Usage

asHampel(bound = Inf, biastype = symmetricBias(), normtype = NormType())

Arguments

Value

Object of class asHampel

Author(s)

Matthias Kohl [email protected]

References

Hampel et al. (1986) Robust Statistics. The Approach Based on Influence Functions. New York: Wiley.

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

asHampel-class

Examples

asHampel()

## The function is currently defined as
function(bound = Inf, biastype = symmetricBias(), normtype = NormType()){ 
    new("asHampel", bound = bound, biastype = biastype, normtype = normtype) }

Description

Class of asymptotic Hampel risk which is the trace of the asymptotic covariance subject to a given bias bound (bound on gross error sensitivity).

Objects from the Class

Objects can be created by calls of the form new("asHampel", ...). More frequently they are created via the generating function asHampel.

Slots

type

Object of class "character": “trace of asymptotic covariance for given bias bound”.

bound

Object of class "numeric": given positive bias bound.

biastype

Object of class "BiasType": symmetric, one-sided or asymmetric

Extends

Class "asRiskwithBias", directly.
Class "asRisk", by class "asRiskwithBias". Class "RiskType", by class "asRisk".

Methods

bound

signature(object = "asHampel"): accessor function for slot bound.

show

signature(object = "asHampel")

Author(s)

Matthias Kohl [email protected]

References

Hampel et al. (1986) Robust Statistics. The Approach Based on Influence Functions. New York: Wiley.

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

asRisk-class, asHampel

Examples

new("asHampel")

Description

Generates an object of class "asMSE".

Usage

asMSE(biastype = symmetricBias(), normtype = NormType())

Arguments

Value

Object of class "asMSE"

Author(s)

Matthias Kohl [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

asMSE-class

Examples

asMSE()

## The function is currently defined as
function(biastype = symmetricBias(), normtype = NormType()){ 
         new("asMSE", biastype = biastype, normtype = normtype) }

Description

Class of asymptotic mean square error.

Objects from the Class

Objects can be created by calls of the form new("asMSE", ...). More frequently they are created via the generating function asMSE.

Slots

type

Object of class "character": “asymptotic mean square error”.

biastype

Object of class "BiasType": symmetric, one-sided or asymmetric

normtype

Object of class "NormType": norm in which a multivariate parameter is considered

Extends

Class "asGRisk", directly.
Class "asRiskwithBias", by class "asGRisk".
Class "asRisk", by class "asRiskwithBias".
Class "RiskType", by class "asGRisk".

Methods

No methods defined with class "asMSE" in the signature.

Author(s)

Matthias Kohl [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

asGRisk-class, asMSE

Examples

new("asMSE")

Description

Class of asymptotic risks.

Objects from the Class

A virtual Class: No objects may be created from it.

Slots

type

Object of class "character".

Extends

Class "RiskType", directly.

Methods

No methods defined with class "asRisk" in the signature.

Author(s)

Matthias Kohl [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Ruckdeschel, P. and Rieder, H. (2004) Optimal Influence Curves for General Loss Functions. Statistics & Decisions (submitted).

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

RiskType-class

Description

Class of asymptotic risks.

Objects from the Class

A “virtual” Class (although it does not contain "VIRTUAL"): No objects may be created from it.

Slots

type

Object of class "character".

biastype

Object of class "BiasType".

normtype

Object of class "NormType".

Extends

Class "RiskType", directly.

Methods

biastype

signature(object = "asRiskwithBias"): accessor function for slot biastype.

biastype<-

signature(object = "asRiskwithBias", value = "BiasType"): replacement function for slot biastype.

normtype

signature(object = "asRiskwithBias"): accessor function for slot normtype.

normtype<-

signature(object = "asRiskwithBias", value = "NormType"): replacement function for slot normtype.

norm

signature(object = "asRiskwithBias"): accessor function for slot fct of slot norm.

Author(s)

Matthias Kohl [email protected], Peter Ruckdeschel [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Ruckdeschel, P. and Rieder, H. (2004) Optimal Influence Curves for General Loss Functions. Statistics & Decisions 22, 201-223.

Ruckdeschel, P. (2005) Optimally One-Sided Bounded Influence Curves. Mathematical Methods in Statistics 14(1), 105-131.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

asRisk-class

Description

Generates an object of class "asSemivar".

Usage

asSemivar(sign = 1)

Arguments

Value

Object of class "asSemivar"

Author(s)

Peter Ruckdeschel [email protected]

References

Ruckdeschel, P. (2005) Optimally One-Sided Bounded Influence Curves. Mathematical Methods in Statistics 14(1), 105-131.

See Also

onesidedBias-class

Examples

asSemivar()

Description

Class for semi-variance risk.

Objects from the Class

Objects can be created by calls of the form new("asSemivar", ...). More frequently they are created via the generating function asSemivar.

Slots

type

Object of class "character": “asymptotic mean square error”.

biastype

Object of class "BiasType": symmetric, one-sided or asymmetric

normtype

Object of class "NormType": norm in which a multivariate parameter is considered

Methods

sign

signature(object = "asSemivar"): accessor function for slot sign.

sign<-

signature(object = "asSemivar", value = "numeric"): replacement function for slot sign.

Extends

Class "asGRisk", directly.
Class "asRiskwithBias", by class "asGRisk".
Class "asRisk", by class "asRiskwithBias".
Class "RiskType", by class "asGRisk".

Author(s)

Peter Ruckdeschel [email protected]

References

Ruckdeschel, P. (2005) Optimally One-Sided Bounded Influence Curves. Mathematical Methods in Statistics 14(1), 105-131.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

asGRisk-class, asMSE

Examples

asSemivar()

Description

Generates an object of class "asUnOvShoot".

Usage

asUnOvShoot(width = 1.960, biastype = symmetricBias())

Arguments

Value

Object of class "asUnOvShoot"

Author(s)

Matthias Kohl [email protected]

References

Rieder, H. (1980) Estimates derived from robust tests. Ann. Stats. 8: 106–115.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

asUnOvShoot-class

Examples

asUnOvShoot()

## The function is currently defined as
function(width = 1.960, biastype = symmetricBias()){ 
     new("asUnOvShoot", width = width, biastype = biastype) }

Description

Class of asymptotic under-/overshoot probability.

Objects from the Class

Objects can be created by calls of the form new("asUnOvShoot", ...). More frequently they are created via the generating function asUnOvShoot.

Slots

type

Object of class "character": “asymptotic under-/overshoot probability”.

width

Object of class "numeric": half the width of given confidence interval.

biastype

Object of class "BiasType": symmetric, one-sided or asymmetric

Extends

Class "asGRisk", directly.
Class "asRiskwithBias", by class "asGRisk".
Class "asRisk", by class "asRiskwithBias".
Class "RiskType", by class "asGRisk".

Methods

width

signature(object = "asUnOvShoot"): accessor function for slot width.

show

signature(object = "asUnOvShoot")

Author(s)

Matthias Kohl [email protected]

References

Rieder, H. (1980) Estimates derived from robust tests. Ann. Stats. 8: 106–115.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

asGRisk-class

Examples

new("asUnOvShoot")

Description

Generates an object of class "asymmetricBias".

Usage

asymmetricBias(name = "asymmetric Bias", nu = c(1,1) )

Arguments

Value

Object of class "asymmetricBias"

Author(s)

Peter Ruckdeschel [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Ruckdeschel, P. (2005) Optimally One-Sided Bounded Influence Curves. Mathematical Methods in Statistics 14(1), 105-131.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

asymmetricBias-class

Examples

asymmetricBias()

## The function is currently defined as
function(){ new("asymmetricBias", name = "asymmetric Bias", nu = c(1,1)) }

Description

Class of asymmetric bias types.

Objects from the Class

Objects can be created by calls of the form new("asymmetricBias", ...). More frequently they are created via the generating function asymmetricBias.

Slots

name

Object of class "character".

nu

Object of class "numeric"; to be in (0,1] x (0,1] with maximum 1; weights for negative and positive bias, respectively

Methods

nu

signature(object = "asymmetricBias"): accessor function for slot nu.

nu<-

signature(object = "asymmetricBias", value = "numeric"): replacement function for slot nu.

Extends

Class "BiasType", directly.

Author(s)

Peter Ruckdeschel [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Ruckdeschel, P. (2005) Optimally One-Sided Bounded Influence Curves. Mathematical Methods in Statistics 14(1), 105-131.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

BiasType-class

Examples

asymmetricBias()
## The function is currently defined as
function(){ new("asymmetricBias", name = "asymmetric Bias", nu = c(1,1)) }

aB <- asymmetricBias()
nu(aB)
try(nu(aB) <- -2) ## error
nu(aB) <- c(0.3,1)

Description

Generates an object of class "L2ParamFamily" which represents a Beta family.

Usage

BetaFamily(shape1 = 1, shape2 = 1, trafo, withL2derivDistr = TRUE)

Arguments

Details

The slots of the corresponding L2 differentiable parameteric family are filled.

Value

Object of class "L2ParamFamily"

Author(s)

Peter Ruckdeschel [email protected]

See Also

L2ParamFamily-class, Beta-class

Examples

(B1 <- BetaFamily())
FisherInfo(B1)
## IGNORE_RDIFF_BEGIN
checkL2deriv(B1)
## IGNORE_RDIFF_END

Description

Class of bias types.

Objects from the Class

A virtual Class: No objects may be created from it.

Slots

name

Object of class "character".

Methods

name

signature(object = "BiasType"): accessor function for slot name.

name<-

signature(object = "BiasType", value = "character"): replacement function for slot name.

Author(s)

Peter Ruckdeschel [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Ruckdeschel, P. (2005) Optimally One-Sided Bounded Influence Curves. Mathematical Methods in Statistics 14(1), 105-131.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

RiskType-class

Examples

aB <- positiveBias()
name(aB)

Description

Generates an object of class "L2ParamFamily" which represents a Binomial family where the probability of success is the parameter of interest.

Usage

BinomFamily(size = 1, prob = 0.5, trafo)

Arguments

Details

The slots of the corresponding L2 differentiable parameteric family are filled.

Value

Object of class "L2ParamFamily"

Author(s)

Matthias Kohl [email protected]

References

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

L2ParamFamily-class, Binom-class

Examples

(B1 <- BinomFamily(size = 25, prob = 0.25))
plot(B1)
FisherInfo(B1)
checkL2deriv(B1)

Description

Generates an object of class "L2LocationFamily" which represents a Cauchy location family.

Usage

CauchyLocationFamily(loc = 0, scale = 1, trafo)

Arguments

Details

The slots of the corresponding L2 differentiable parameteric family are filled.

Value

Object of class "L2LocationScaleFamily"

Author(s)

Peter Ruckdeschel [email protected]

References

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

L2ParamFamily-class, Cauchy-class

Examples

(C1 <- CauchyLocationFamily())
plot(C1)
FisherInfo(C1)
### need smaller integration range:
checkL2deriv(C1)

Description

Generates an object of class "L2LocationScaleFamily" which represents a Cauchy location and scale family.

Usage

CauchyLocationScaleFamily(loc = 0, scale = 1, trafo)

Arguments

Details

The slots of the corresponding L2 differentiable parameteric family are filled.

Value

Object of class "L2LocationScaleFamily"

Author(s)

Matthias Kohl [email protected]

References

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

L2ParamFamily-class, Cauchy-class

Examples

(C1 <- CauchyLocationScaleFamily())
## synonymous: C1 <- CauchyFamily()
plot(C1)
FisherInfo(C1)
### need smaller integration range:
distrExoptions("ElowerTruncQuantile"=1e-4,"EupperTruncQuantile"=1e-4)
checkL2deriv(C1)
distrExoptions("ElowerTruncQuantile"=1e-7,"EupperTruncQuantile"=1e-7)

Description

Generic function for checking the L2-derivative of an L2-differentiable family of probability measures.

Usage

checkL2deriv(L2Fam, ...)
## S3 method for class 'relMatrix'
print(x,...)

Arguments

Details

The precisions of the centering and the Fisher information are computed.

Value

A list with items maximum.deviation, cent, consist, and condition is invisibly returned, where maximum.deviation comprises the maximal absolute value of all entries in cent and consist, cent shows the expectation of L2deriv(L2Fam) (which should be 0), consist shows the difference between the Fisher information and cov(L2deriv(L2Fam)) (which should be 0), and condition is the condition number of the Fisher information.

Note

The return value gives the non-rounded values (which will be machine dependent), whereas on argument out==TRUE (the default) we only issue the values up to 5 digits which should be independent of the machine. For the output of relative differences, we adjust accuracy to the size of the maximal (absolute) value of the Fisher information. In case of the consistency condition, at positions where the denominator is 0, we print a "."; this is done through helper S3 method print.relMatrix.

Author(s)

Matthias Kohl [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

L2ParamFamily-class

Examples

F1 <- new("L2ParamFamily")
checkL2deriv(F1)

Description

Return value S4 classes for method “confint”.

Objects from the Class

Objects could in principle be created by calls of the form new("Confint", ...). The preferred form is to have them created via a call to confint.

Slots

type

Object of class "character": type of the confidence interval (asymptotic, bootstrap,...). Can be of length >2. Then in printing, the first element is printed in the gap '[...]' in 'an [...] confidence interval', while the other elements are printed below.

confint

Object of class "array": the confidence interval(s).

call.estimate

Object of class "call": the estimate(s) for which the confidence intervals are produced.

name.estimate

Object of class "character": the name of the estimate(s) for which the confidence intervals are produced.

samplesize.estimate:

Object of class "numeric": the sample size of the estimate(s) for which the confidence intervals are (only complete cases) produced.

completecases.estimate:

Object of class "logical": complete cases at which the estimate was evaluated.

trafo.estimate

Object of class "matrix": the trafo/derivative matrix of the estimate(s) for which the confidence intervals are produced.

nuisance.estimate

Object of class "OptionalNumeric": the nuisance parameter (if any) at which the confidence intervals are produced.

fixed.estimate

Object of class "OptionalNumeric": the fixed part of the parameter (if any) at which the confidence intervals are produced.

Methods

type

signature(object = "Confint"): accessor function for slot type.

confint

signature(object = "Confint", method = "missing"): accessor function for slot type.

call.estimate

signature(object = "Confint"): accessor function for slot call.estimate.

name.estimate

signature(object = "Confint"): accessor function for slot name.estimate.

trafo.estimate

signature(object = "Confint"): accessor function for slot trafo.estimate.

samplesize.estimate

signature(object = "Confint"): (with additional argument onlycompletecases defaulting to TRUE returns the sample size; in case there are any incomplete cases and argument onlycompletecases is FALSE, the number of these is added to slot samplesize.

completecases.estimate

signature(object = "Confint"): accessor function for slot completecases.estimate.

nuisance.estimate

signature(object = "Confint"): accessor function for slot nuisance.estimate.

fixed.estimate

signature(object = "Confint"): accessor function for slot fixed.estimate.

show

signature(object = "Confint"): shows a detailed view of the object; slots nuisance.estimate and fixed.estimate are only shown if non-null, and slot trafo.estimate only if different from a unit matrix.

print

signature(object = "Confint"): just as show, but with additional arguments digits.

Details for methods 'show', 'print'

Detailedness of output by methods show, print is controlled by the global option show.details to be set by distrModoptions.

As method show is used when inspecting an object by typing the object's name into the console, show comes without extra arguments and hence detailedness must be controlled by global options.

Method print may be called with a (partially matched) argument show.details, and then the global option is temporarily set to this value.

More specifically, when show.detail is matched to "minimal" you will be shown only the type of the confidence interval(s) and its/their values. When show.detail is matched to "medium", you will in addition see the type of the estimator(s) for which it is produced, the corresponding call of the estimater, its sample size, and, if present, the value of the corresponding nuisance parameter. Finally, when show.detail is matched to "maximal", additionally you will be shown the fixed part of the parameter (if present) and the transformation of the estimator (if non-trivial, i.e. the identity) in form of its function code respectively of its derivative matrix.

Note

The pretty-printing code for methods show and print has been borrowed from confint.default in package stats.

Author(s)

Peter Ruckdeschel [email protected]

See Also

Estimator, confint, Estimate-class, trafo-methods

Examples

## some transformation
mtrafo <- function(x){
     nms0 <- c("scale","shape")
     nms <- c("shape","rate")
     fval0 <- c(x[2], 1/x[1])
     names(fval0) <- nms
     mat0 <- matrix( c(0, -1/x[1]^2, 1, 0), nrow = 2, ncol = 2,
                     dimnames = list(nms,nms0))                          
     list(fval = fval0, mat = mat0)}

x <- rgamma(50, scale = 0.5, shape = 3)

## parametric family of probability measures
G <- GammaFamily(scale = 1, shape = 2, trafo = mtrafo)
## MLE
res <- MLEstimator(x = x, ParamFamily = G)
ci <- confint(res)
print(ci, digits = 4, show.details="maximal")
print(ci, digits = 4, show.details="medium")
print(ci, digits = 4, show.details="minimal")

Description

Methods for function confint in package distrMod; by default uses confint and its corresponding S3-methods, but also computes (asymptotic) confidence intervals for objects of class Estimate. Computes confidence intervals for one or more parameters in a fitted model.

Usage

confint(object, method, ...)
## S4 method for signature 'ANY,missing'
confint(object, method, parm, level = 0.95, ...)
## S4 method for signature 'Estimate,missing'
confint(object, method, level = 0.95)
## S4 method for signature 'mle,missing'
confint(object, method, parm, level = 0.95, ...)
## S4 method for signature 'profile.mle,missing'
confint(object, method, parm, level = 0.95, ...)

Arguments

Details

confint is a generic function. Its behavior differs according to its arguments.

signature ANY,missing:

the default method; uses the S3 generic of package stats, see confint; its return value is a matrix (or vector) with columns giving lower and upper confidence limits for each parameter. These will be labelled as (1-level)/2 and 1 - (1-level)/2 in % (by default 2.5% and 97.5%).

signature Estimate,missing:

will return an object of class Confint which corresponds to a confidence interval assuming asymptotic normality, and hence needs suitably filled slot asvar in argument object. Besides the actual bounds, organized in an array just as in the S3 generic, the return value also captures the name of the estimator for which it is produced, as well as the corresponding call producing the estimator, and the corresponding trafo and nuisance slots/parts.

See Also

confint, confint.glm and confint.nls in package MASS, Confint-class.

Examples

## for signature ANY examples confer stats::confint
## (empirical) Data
x <- rgamma(50, scale = 0.5, shape = 3)

## parametric family of probability measures
G <- GammaFamily(scale = 1, shape = 2)

## Maximum likelihood estimator
res <- MLEstimator(x = x, ParamFamily = G)
confint(res)

### for comparison:
require(MASS)
(res1 <- fitdistr(x, "gamma"))
## add a convenient (albeit wrong)
## S3-method for vcov:
## --- wrong as in general cov-matrix
##     will not be diagonal
## but for conf-interval this does
## not matter...
vcov.fitdistr <- function(object, ...){
     v<-diag(object$sd^2)
     rownames(v) <- colnames(v) <- names(object$estimate) 
     v}

## explicitely transforming to
## MASS parametrization:
mtrafo <- function(x){
     nms0 <- names(c(main(param(G)),nuisance(param(G))))
     nms <- c("shape","rate")
     fval0 <- c(x[2], 1/x[1])
     names(fval0) <- nms
     mat0 <- matrix( c(0, -1/x[1]^2, 1, 0), nrow = 2, ncol = 2,
                     dimnames = list(nms,nms0))                          
     list(fval = fval0, mat = mat0)}

G2 <- G
trafo(G2) <- mtrafo
res2 <- MLEstimator(x = x, ParamFamily = G2)

old<-getdistrModOption("show.details")
distrModoptions("show.details" = "minimal")
res
res1
res2
confint(res)
confint(res1)
confint(res2)
confint(res,level=0.99)
distrModoptions("show.details" = old)

Description

Provides information on the (intended) masking of and (non-intended) masking by other other functions in package distrMod

Usage

distrModMASK(library = NULL)

Arguments

Value

no value is returned

Author(s)

Peter Ruckdeschel [email protected]

Examples

## IGNORE_RDIFF_BEGIN
distrModMASK()
## IGNORE_RDIFF_END

Description

With distrModOptions you can inspect and change the global variables of the package distrMod.

Usage

distrModOptions(...)
getdistrModOption(x)
distrModoptions(...)

Arguments

Details

Invoking distrModoptions() with no arguments returns a list with the current values of the options. To access the value of a single option, one should use getdistrModOption("show.details"), e.g., rather than distrModoptions("show.details") which is a list of length one.

Value

distrModoptions() returns a list of the global options of distrMod.
distrModoptions("show.details") returns the global option show.details as a list of length 1.
distrModoptions("show.details" = "minimal") sets the value of the global option show.details to "minimal". getdistrModOption("show.details") the current value set for option show.details.

distrModoptions

For compatibility with spelling in package distr, distrModoptions is just a synonym to distrModoptions.

Currently available options

show.details

degree of detailedness for method show for objects of classes of the distrXXX family of packages. Possible values are

"maximal"

all information is shown

"minimal"

only the most important information is shown

"medium"

somewhere in the middle; see actual show-methods for details.

The default value is "maximal".

Author(s)

Matthias Kohl [email protected],
Peter Ruckdeschel [email protected]

See Also

options, getOption, distroptions, getdistrOption

Examples

distrModoptions()
distrModoptions("show.details")
distrModoptions("show.details" = "maximal")
distrModOptions("show.details" = "minimal")
# or
getdistrModOption("show.details")

Description

Class of estimates.

Objects from the Class

Objects can be created by calls of the form new("Estimate", ...). More frequently they are created via the generating function Estimator.

Slots

name

Object of class "character": name of the estimator.

estimate

Object of class "ANY": estimate.

estimate.call

Object of class "call": call by which estimate was produced.

Infos

object of class "matrix" with two columns named method and message: additional informations.

asvar

object of class "OptionalNumericOrMatrix" which may contain the asymptotic (co)variance of the estimator.

samplesize

object of class "numeric" — the samplesize (only complete cases are counted) at which the estimate was evaluated.

completecases

object of class "logical" — complete cases at which the estimate was evaluated.

nuis.idx

object of class "OptionalNumeric": indices of estimate belonging to the nuisance part.

fixed

object of class "OptionalNumeric": the fixed and known part of the parameter.

trafo

object of class "list": a list with components fct and mat (see below).

untransformed.estimate

Object of class "ANY": untransformed estimate.

untransformed.asvar

object of class "OptionalNumericOrMatrix" which may contain the asymptotic (co)variance of the untransformed estimator.

Methods

name

signature(object = "Estimate"): accessor function for slot name.

name<-

signature(object = "Estimate"): replacement function for slot name.

estimate

signature(object = "Estimate"): accessor function for slot estimate.

untransformed.estimate

signature(object = "Estimate"): accessor function for slot untransformed.estimate.

estimate.call

signature(object = "Estimate"): accessor function for slot estimate.call.

samplesize

signature(object = "Estimate"): (with additional argument onlycompletecases defaulting to TRUE returns the sample size; in case there are any incomplete cases and argument onlycompletecases is FALSE, the number of these is added to slot samplesize.

completecases

signature(object = "Estimate"): accessor function for slot completecases.

asvar

signature(object = "Estimate"): accessor function for slot asvar.

asvar<-

signature(object = "Estimate"): replacement function for slot asvar.

untransformed.asvar

signature(object = "Estimate"): accessor function for slot untransformed.asvar.

nuisance

signature(object = "Estimate"): accessor function for nuisance part of slot estimate.

main

signature(object = "Estimate"): accessor function for main part of slot estimate.

fixed

signature(object = "Estimate"): accessor function for slot fixed.

Infos

signature(object = "Estimate"): accessor function for slot Infos.

Infos<-

signature(object = "Estimate"): replacement function for slot Infos.

addInfo<-

signature(object = "Estimate"): function to add an information to slot Infos.

show

signature(object = "Estimate")

print

signature(object = "Estimate"): just as show, but with additional arguments digits.

Details for methods 'show', 'print'

Detailedness of output by methods show, print is controlled by the global option show.details to be set by distrModoptions.

As method show is used when inspecting an object by typing the object's name into the console, show comes without extra arguments and hence detailedness must be controlled by global options.

Method print may be called with a (partially matched) argument show.details, and then the global option is temporarily set to this value.

More specifically, when show.detail is matched to "minimal" you will be shown only the name/type of the estimator, the value of its main part, and, if present, the corresponding standard errors, as well as, also if present, the value of the nuisance part. When show.detail is matched to "medium", you will in addition see the class of the estimator, its call and its sample-size and, if present, the fixed part of the parameter and the asymptotic covariance matrix. Also the information gathered in the Infos slot is shown. Finally, when show.detail is matched to "maximal", and if, in addition, you estimate non-trivial (i.e. not the identity) transformation of the parameter of the parametric family, you will also be shown this transformation in form of its function and its derivative matrix at the estimated parameter value, as well as the estimator (with standard errors, if present) and (again, if present) the corresponding asymptotic covariance of the untransformed, total (i.e. main and nuisance part) parameter.

trafo realizes partial influence curves; i.e.; we are only interested is some possibly lower dimensional smooth (not necessarily linear or even coordinate-wise) aspect/transformation $\tau$ of the parameter $\theta$.

To be coherent with the corresponding nuisance implementation, we make the following convention:

The full parameter $\theta$ is split up coordinate-wise in a main parameter $\theta'$ and a nuisance parameter $\theta''$ (which is unknown, too, hence has to be estimated, but only is of secondary interest) and a fixed, known part $\theta'''$.

Without loss of generality, we restrict ourselves to the case that transformation $\tau$ only acts on the main parameter $\theta'$ — if we want to transform the whole parameter, we only have to assume that both nuisance parameter $\theta''$ and fixed, known part of the parameter $\theta'''$ have length 0.

To the implementation:

Slot trafo can either contain a (constant) matrix $D_\theta$ or a function

$\tau\colon \Theta' \to \tilde \Theta,\qquad \theta \mapsto \tau(\theta)$

mapping main parameter $\theta'$ to some range $\tilde \Theta$.

If slot value trafo is a function, besides $\tau(\theta)$, it will also return the corresponding derivative matrix $\frac{\partial}{\partial \theta}\tau(\theta)$. More specifically, the return value of this function theta is a list with entries fval, the function value $\tau(\theta)$, and mat, the derivative matrix.

In case trafo is a matrix $D$, we interpret it as such a derivative matrix $\frac{\partial}{\partial \theta}\tau(\theta)$, and, correspondingly, $\tau(\theta)$ as the linear mapping $\tau(\theta)=D\,\theta$.

Note

The pretty-printing code for methods show and print has been borrowed from print.fitdistr in package MASS by B.D. Ripley.

Author(s)

Matthias Kohl [email protected],
Peter Ruckdeschel [email protected]

See Also

Estimator

Examples

x <- rnorm(100)
Estimator(x, estimator = mean, name = "mean")

x1 <- x; x1[sample(1:100,10)] <- NA
myEst1 <- Estimator(x1, estimator = mean, name = "mean")
samplesize(myEst1)
samplesize(myEst1, onlycomplete = FALSE)

Description

The function Estimator provides a general way to compute estimates.

Usage

Estimator(x, estimator, name, Infos, asvar = NULL, nuis.idx,
          trafo = NULL, fixed = NULL, asvar.fct, na.rm = TRUE, ...,
          ParamFamily = NULL, .withEvalAsVar = TRUE)

Arguments

Details

The argument criterion has to be a function with arguments the empirical data as well as an object of class "Distribution" and possibly ....

Value

An object of S4-class "Estimate".

Author(s)

Matthias Kohl [email protected],
Peter Ruckdeschel [email protected]

See Also

Estimate-class

Examples

x <- rnorm(100)
Estimator(x, estimator = mean, name = "mean")

X <- matrix(rnorm(1000), nrow = 10)
Estimator(X, estimator = rowMeans, name = "mean")

Description

Generates an object of class "EvenSymmetric".

Usage

EvenSymmetric(SymmCenter = 0)

Arguments

Value

Object of class "EvenSymmetric"

Author(s)

Matthias Kohl [email protected]

See Also

EvenSymmetric-class, FunctionSymmetry-class

Examples

EvenSymmetric()

## The function is currently defined as
function(SymmCenter = 0){ 
    new("EvenSymmetric", SymmCenter = SymmCenter) 
}

Description

Class for even functions.

Objects from the Class

Objects can be created by calls of the form new("EvenSymmetric"). More frequently they are created via the generating function EvenSymmetric.

Slots

type

Object of class "character": contains “even function”

SymmCenter

Object of class "numeric": center of symmetry

Extends

Class "FunctionSymmetry", directly.
Class "Symmetry", by class "FunctionSymmetry".

Author(s)

Matthias Kohl [email protected]

See Also

EvenSymmetric, FunctionSymmetry-class

Examples

new("EvenSymmetric")

Description

existsPIC-methods to check whether in a given L2 differentiable model at parameter value theta there exist (partial) influence curves to Trafo $D_\theta$.

Usage

existsPIC(object, ...)
## S4 method for signature 'L2ParamFamily'
existsPIC(object, warning = TRUE, tol = .Machine$double.eps^.5)

Arguments

Details

To check the existence of (partial) influence curves and, simultaneously, for bounded (partial) influence curves, by Lemma 1.1.3 in Kohl(2005) [resp. the fact that ${\rm ker} I={\rm ker} J$ for $J= {\rm E} (\Lambda',1)' (\Lambda',1) w$ and $w={\rm min}(1, b/|(\Lambda',1)|$], it suffices to check that ${\rm ker }I$ is a subset of ${\rm ker }D_\theta$. This is done by a call to isKerAinKerB.

Author(s)

Peter Ruckdeschel [email protected]

References

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

isKerAinKerB

Description

Generates an object of class "L2ScaleFamily" which represents an exponential scale family.

Usage

ExpScaleFamily(scale = 1, trafo)

Arguments

Details

The slots of the corresponding L2 differentiable parameteric family are filled. The scale parameter corresponds to $1/\code{rate}$.

Value

Object of class "L2ScaleFamily"

Author(s)

Matthias Kohl [email protected]

References

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

L2ParamFamily-class, Exp-class

Examples

(E1 <- ExpScaleFamily())
plot(E1)
Map(L2deriv(E1)[[1]])
## IGNORE_RDIFF_BEGIN
checkL2deriv(E1)
## IGNORE_RDIFF_END

Description

Generates an object of class "fiBias".

Usage

fiBias()

Value

Object of class "fiBias"

Author(s)

Matthias Kohl [email protected]

References

Ruckdeschel, P. and Kohl, M. (2005) How to approximate the finite sample risk of M-estimators.

See Also

fiBias-class

Examples

fiBias()

## The function is currently defined as
function(){ new("fiBias") }

Description

Class of finite-sample bias.

Objects from the Class

Objects can be created by calls of the form new("fiBias", ...). More frequently they are created via the generating function fiBias.

Slots

type

Object of class "character": “finite-sample bias”.

Extends

Class "fiRisk", directly.
Class "RiskType", by class "fiRisk".

Methods

No methods defined with class "fiBias" in the signature.

Author(s)

Matthias Kohl [email protected]

References

Ruckdeschel, P. and Kohl, M. (2005) How to approximate the finite sample risk of M-estimators.

See Also

fiRisk-class, fiBias

Examples

new("fiBias")

Description

Generates an object of class "fiCov".

Usage

fiCov()

Value

Object of class "fiCov"

Author(s)

Matthias Kohl [email protected]

References

Ruckdeschel, P. and Kohl, M. (2005) How to approximate the finite sample risk of M-estimators.

See Also

fiCov-class

Examples

fiCov()

## The function is currently defined as
function(){ new("fiCov") }

Description

Class of finite-sample covariance.

Objects from the Class

Objects can be created by calls of the form new("fiCov", ...). More frequently they are created via the generating function fiCov.

Slots

type

Object of class "character": “finite-sample covariance”.

Extends

Class "fiRisk", directly.
Class "RiskType", by class "fiRisk".

Methods

No methods defined with class "fiCov" in the signature.

Author(s)

Matthias Kohl [email protected]

References

Ruckdeschel, P. and Kohl, M. (2005) How to approximate the finite sample risk of M-estimators.

See Also

fiRisk-class, fiCov

Examples

new("fiCov")

Description

Generates an object of class "fiHampel".

Usage

fiHampel(bound = Inf)

Arguments

Value

Object of class fiHampel

Author(s)

Matthias Kohl [email protected]

References

Hampel et al. (1986) Robust Statistics. The Approach Based on Influence Functions. New York: Wiley.

Ruckdeschel, P. and Kohl, M. (2005) How to approximate the finite sample risk of M-estimators.

See Also

fiHampel-class

Examples

fiHampel()

## The function is currently defined as
function(bound = Inf){ new("fiHampel", bound = bound) }

Description

Class of finite-sample Hampel risk which is the trace of the finite-sample covariance subject to a given bias bound (bound on gross error sensitivity).

Objects from the Class

Objects can be created by calls of the form new("fiHampel", ...). More frequently they are created via the generating function fiHampel.

Slots

type

Object of class "character": “trace of finite-sample covariance for given bias bound”.

bound

Object of class "numeric": given positive bias bound.

Extends

Class "fiRisk", directly.
Class "RiskType", by class "fiRisk".

Methods

bound

signature(object = "fiHampel"): accessor function for slot bound.

show

signature(object = "fiHampel")

Author(s)

Matthias Kohl [email protected]

References

Hampel et al. (1986) Robust Statistics. The Approach Based on Influence Functions. New York: Wiley.

Ruckdeschel, P. and Kohl, M. (2005) How to approximate the finite sample risk of M-estimators.

See Also

fiRisk-class, fiHampel

Examples

new("fiHampel")

Description

Generates an object of class "fiMSE".

Usage

fiMSE()

Value

Object of class "fiMSE"

Author(s)

Matthias Kohl [email protected]

References

Ruckdeschel, P. and Kohl, M. (2005) How to approximate the finite sample risk of M-estimators.

See Also

fiMSE-class

Examples

fiMSE()

## The function is currently defined as
function(){ new("fiMSE") }

Description

Class of asymptotic mean square error.

Objects from the Class

Objects can be created by calls of the form new("fiMSE", ...). More frequently they are created via the generating function fiMSE.

Slots

type

Object of class "character": “finite-sample mean square error”.

Extends

Class "fiRisk", directly.
Class "RiskType", by class "fiRisk".

Methods

No methods defined with class "fiMSE" in the signature.

Author(s)

Matthias Kohl [email protected]

References

Ruckdeschel, P. and Kohl, M. (2005) How to approximate the finite sample risk of M-estimators.

See Also

fiRisk-class, fiMSE

Examples

new("fiMSE")

Description

Class of finite-sample risks.

Objects from the Class

A virtual Class: No objects may be created from it.

Slots

type

Object of class "character".

Extends

Class "RiskType", directly.

Methods

No methods defined with class "fiRisk" in the signature.

Author(s)

Matthias Kohl [email protected]

References

Ruckdeschel, P. and Kohl, M. (2005) How to approximate the finite sample risk of M-estimators.

See Also

RiskType-class

Description

Generates an object of class "fiUnOvShoot".

Usage

fiUnOvShoot(width = 1.960)

Arguments

Value

Object of class "fiUnOvShoot"

Author(s)

Matthias Kohl [email protected]

References

Huber, P.J. (1968) Robust Confidence Limits. Z. Wahrscheinlichkeitstheor. Verw. Geb. 10:269–278.

Rieder, H. (1989) A finite-sample minimax regression estimator. Statistics 20(2): 211–221.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

Ruckdeschel, P. and Kohl, M. (2005) How to approximate the finite sample risk of M-estimators.

See Also

fiUnOvShoot-class

Examples

fiUnOvShoot()

## The function is currently defined as
function(width = 1.960){ new("fiUnOvShoot", width = width) }

Description

Class of finite-sample under-/overshoot probability.

Objects from the Class

Objects can be created by calls of the form new("fiUnOvShoot", ...). More frequently they are created via the generating function fiUnOvShoot.

Slots

type

Object of class "character": “finite-sample under-/overshoot probability”.

width

Object of class "numeric": half the width of given confidence interval.

Extends

Class "fiRisk", directly.
Class "RiskType", by class "fiRisk".

Methods

width

signature(object = "fiUnOvShoot"): accessor function for slot width.

show

signature(object = "fiUnOvShoot")

Author(s)

Matthias Kohl [email protected]

References

Huber, P.J. (1968) Robust Confidence Limits. Z. Wahrscheinlichkeitstheor. Verw. Geb. 10:269–278.

Rieder, H. (1989) A finite-sample minimax regression estimator. Statistics 20(2): 211–221.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

Ruckdeschel, P. and Kohl, M. (2005) Computation of the Finite Sample Risk of M-estimators on Neighborhoods.

See Also

fiRisk-class

Examples

new("fiUnOvShoot")

Description

Class of symmetries for functions.

Objects from the Class

A virtual Class: No objects may be created from it.

Slots

type

Object of class "character": discribes type of symmetry.

SymmCenter

Object of class "OptionalNumeric": center of symmetry.

Extends

Class "Symmetry", directly.

Author(s)

Matthias Kohl [email protected]

See Also

Symmetry-class, OptionalNumeric-class

Description

Generates an object of class "FunSymmList".

Usage

FunSymmList(...)

Arguments

Value

Object of class "FunSymmList"

Author(s)

Matthias Kohl [email protected]

See Also

FunSymmList-class

Examples

FunSymmList(NonSymmetric(), EvenSymmetric(SymmCenter = 1), 
            OddSymmetric(SymmCenter = 2))

## The function is currently defined as
function (...){
    new("FunSymmList", list(...))
}

Description

Create a list of symmetries for a list of functions

Objects from the Class

Objects can be created by calls of the form new("FunSymmList", ...). More frequently they are created via the generating function FunSymmList.

Slots

.Data

Object of class "list". A list of objects of class "FunctionSymmetry".

Extends

Class "list", from data part.
Class "vector", by class "list".

Author(s)

Matthias Kohl [email protected]

See Also

FunctionSymmetry-class

Examples

new("FunSymmList", list(NonSymmetric(), EvenSymmetric(SymmCenter = 1), 
                        OddSymmetric(SymmCenter = 2)))

Description

Generates an object of class "L2ParamFamily" which represents a Gamma family.

Usage

GammaFamily(scale = 1, shape = 1, trafo, withL2derivDistr = TRUE)

Arguments

Details

The slots of the corresponding L2 differentiable parameteric family are filled.

Value

Object of class "L2ParamFamily"

Author(s)

Matthias Kohl [email protected]

References

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

L2ParamFamily-class, Gammad-class

Examples

(G1 <- GammaFamily())
FisherInfo(G1)
## IGNORE_RDIFF_BEGIN
checkL2deriv(G1)
## IGNORE_RDIFF_END

Description

Generates an object of class "InfoNorm" — used for information-standardized influence curves.

Usage

InfoNorm()

Value

Object of class "InfoNorm"

Author(s)

Matthias Kohl [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

InfoNorm-class

Examples

## IGNORE_RDIFF_BEGIN
InfoNorm()

## The function is currently defined as
function(){ new("InfoNorm") }
## IGNORE_RDIFF_END

Description

For two matrices A and B checks whether the null space of A is a subspace of the null space of B, in other words, if $Ax=0$ entails Bx=0.

Usage

isKerAinKerB(A, B, tol = .Machine$double.eps)

Arguments

Details

via calls to svd, the projectors $\pi_A$ and $\pi_B$ onto the respective orthogonal complements of ${\rm ker}(A)$ and ${\rm ker}(B)$ are calculated and then is checked whether $\pi_B\pi_A=\pi_B$.

Value

logical

Author(s)

Peter Ruckdeschel [email protected]

Examples

ma <- cbind(1,1,c(1,1,7))
D <- t(ma %*% c(0,1,-1))
## IGNORE_RDIFF_BEGIN
## note that results may vary according to BLAS
isKerAinKerB(D,ma)
isKerAinKerB(ma,D)
## IGNORE_RDIFF_END

Description

Class of L2 differentiable parametric group families.

Objects from the Class

Objects can be created by calls of the form new("L2GroupParamFamily", ...). More frequently, this class is just used as an intermediate class to classes of specific group models like L2LocationFamily-class, L2ScaleFamily-class, and L2LocationScaleFamily-class.

Slots

name

[inherited from class "ProbFamily"] object of class "character": name of the family.

distribution

[inherited from class "ProbFamily"] object of class "Distribution": member of the family.

distrSymm

[inherited from class "ProbFamily"] object of class "DistributionSymmetry": symmetry of distribution.

param

[inherited from class "ParamFamily"] object of class "ParamFamParameter": parameter of the family.

fam.call

[inherited from class "ParamFamily"] object of class "call": call by which parametric family was produced.

makeOKPar

[inherited from class "ParamFamily"] object of class "function": has argument param — the (total) parameter, returns valid parameter; used if optim resp. optimize— try to use “illegal” parameter values; then makeOKPar makes a valid parameter value out of the illegal one.

startPar

[inherited from class "ParamFamily"] object of class "function": has argument x — the data, returns starting parameter for optim resp. optimize— a starting estimator in case parameter is multivariate or a search interval in case parameter is univariate.

modifyParam

[inherited from class "ParamFamily"] object of class "function": mapping from the parameter space (represented by "param") to the distribution space (represented by "distribution").

props

[inherited from class "ProbFamily"] object of class "character": properties of the family.

L2deriv

[inherited from class "L2ParamFamily"] object of class "EuclRandVariable": L2 derivative of the family.

L2deriv.fct

[inherited from class "L2ParamFamily"] object of class "function": mapping from the parameter space (argument param of class "ParamFamParameter") to a mapping from observation x to the value of the L2derivative; L2deriv.fct is then used from observation x to value of the L2derivative; L2deriv.fct is used by modifyModel to move the L2deriv according to a change in the parameter

L2derivSymm

[inherited from class "L2ParamFamily"] object of class "FunSymmList": symmetry of the maps included in L2deriv.

L2derivDistr

[inherited from class "L2ParamFamily"] object of class "UnivarDistrList": list which includes the distribution of L2deriv.

L2derivDistrSymm

[inherited from class "L2ParamFamily"] object of class "DistrSymmList": symmetry of the distributions included in L2derivDistr.

FisherInfo.fct

[inherited from class "L2ParamFamily"] object of class "function": mapping from the parameter space (argument param of class "ParamFamParameter") to the set of positive semidefinite matrices; FisherInfo.fct is used by modifyModel to move the Fisher information according to a change in the parameter

FisherInfo

[inherited from class "L2ParamFamily"] object of class "PosDefSymmMatrix": Fisher information of the family.

LogDeriv

object of class "function": has argument x; the negative logarithmic derivative of the density of the model distribution at the "standard" parameter value.

Extends

Class "L2ParamFamily", directly.
Class "ParamFamily", by class "L2ParamFamily".
Class "ProbFamily", by class "ParamFamily".

Methods

LogDeriv

signature(object = "L2GroupParamFamily"): accessor function for slot LogDeriv.

LogDeriv<-

signature(object = "L2GroupParamFamily"): replacement function for slot LogDeriv.

Author(s)

Peter Ruckdeschel [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

L2ParamFamily-class, ParamFamily-class

Examples

F1 <- new("L2GroupParamFamily")
plot(F1)

Description

Generates an object of class "L2LocationFamily".

Usage

L2LocationFamily(loc = 0, name, centraldistribution = Norm(),
                 locname = "loc", modParam, LogDeriv,  
                 L2derivDistr.0, FisherInfo.0, distrSymm, L2derivSymm, 
                 L2derivDistrSymm, trafo, .returnClsName = NULL)

Arguments

Details

If name is missing, the default “L2 location family” is used. The function modParam is optional. If it is missing, it is constructed from centraldistribution using the location structure of the model. Slot param is filled accordingly with the argument trafo passed to L2LocationFamily. In case L2derivDistr.0 is missing, L2derivDistr is computed via imageDistr, else L2derivDistr is assigned L2derivDistr.0, coerced to "UnivariateDistributionList". In case FisherInfo.0 is missing, Fisher information is computed from L2deriv using E. If distrSymm is missing, it is set to symmetry about loc. If L2derivSymm is missing, it is set to no symmetry, and if L2derivDistrSymm is missing, it is set to no symmetry, too.

Value

Object of class "L2LocationFamily"

Author(s)

Matthias Kohl [email protected],
Peter Ruckdeschel [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

L2LocationFamily-class

Examples

F1 <- L2LocationFamily()
plot(F1)

Description

Class of L2 differentiable parametric group families.

Objects from the Class

Objects can be created by calls of the form new("L2LocationFamily", ...). More frequently they are created via the generating function L2LocationFamily.

Slots

name

[inherited from class "ProbFamily"] object of class "character": name of the family.

distribution

[inherited from class "ProbFamily"] object of class "Distribution": member of the family.

distrSymm

[inherited from class "ProbFamily"] object of class "DistributionSymmetry": symmetry of distribution.

param

[inherited from class "ParamFamily"] object of class "ParamFamParameter": parameter of the family.

fam.call

[inherited from class "ParamFamily"] object of class "call": call by which parametric family was produced.

makeOKPar

[inherited from class "ParamFamily"] object of class "function": has argument param — the (total) parameter, returns valid parameter; used if optim resp. optimize— try to use “illegal” parameter values; then makeOKPar makes a valid parameter value out of the illegal one.

startPar

[inherited from class "ParamFamily"] object of class "function": has argument x — the data, returns starting parameter for optim resp. optimize— a starting estimator in case parameter is multivariate or a search interval in case parameter is univariate.

modifyParam

[inherited from class "ParamFamily"] object of class "function": mapping from the parameter space (represented by "param") to the distribution space (represented by "distribution").

props

[inherited from class "ProbFamily"] object of class "character": properties of the family.

L2deriv

[inherited from class "L2ParamFamily"] object of class "EuclRandVariable": L2 derivative of the family.

L2deriv.fct

[inherited from class "L2ParamFamily"] object of class "function": mapping from the parameter space (argument param of class "ParamFamParameter") to a mapping from observation x to the value of the L2derivative; L2deriv.fct is then used from observation x to value of the L2derivative; L2deriv.fct is used by modifyModel to move the L2deriv according to a change in the parameter

L2derivSymm

[inherited from class "L2ParamFamily"] object of class "FunSymmList": symmetry of the maps included in L2deriv.

L2derivDistr

[inherited from class "L2ParamFamily"] object of class "UnivarDistrList": list which includes the distribution of L2deriv.

L2derivDistrSymm

[inherited from class "L2ParamFamily"] object of class "DistrSymmList": symmetry of the distributions included in L2derivDistr.

FisherInfo.fct

[inherited from class "L2ParamFamily"] object of class "function": mapping from the parameter space (argument param of class "ParamFamParameter") to the set of positive semidefinite matrices; FisherInfo.fct is used by modifyModel to move the Fisher information according to a change in the parameter

FisherInfo

[inherited from class "L2ParamFamily"] object of class "PosDefSymmMatrix": Fisher information of the family.

LogDeriv

[inherited from class "L2GroupParamFamily"] object of class "function": has argument x; the negative logarithmic derivative of the density of the model distribution at the "standard" parameter value.

locscalename

[inherited from class "L2LocationScaleUnion"] object of class "character": names of location and scale parameter

Extends

Class "L2LocationScaleUnion", directly.
Class "L2GroupParamFamily", by class "L2LocationScaleUnion".
Class "L2ParamFamily", by class "L2GroupParamFamily".
Class "ParamFamily", by class "L2ParamFamily".
Class "ProbFamily", by class "ParamFamily".

Methods

modifyModel

signature(model = "L2LocationFamily", param = "ParamFamParameter"): moves the L2-location family model to parameter param

Author(s)

Matthias Kohl [email protected],
Peter Ruckdeschel [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

L2LocationFamily, ParamFamily-class

Examples

F1 <- new("L2LocationFamily")
plot(F1)

Description

Generates an object of class "L2LocationScaleFamily".

Usage

L2LocationScaleFamily(loc = 0, scale = 1, name, centraldistribution = Norm(),
                      locscalename = c("loc", "scale"), modParam, LogDeriv,  
                      L2derivDistr.0, FisherInfo.0, distrSymm, L2derivSymm, 
                      L2derivDistrSymm, trafo, .returnClsName = NULL)

Arguments

Details

If name is missing, the default “L2 location and scale family” is used. The function modParam is optional. If it is missing, it is constructed from centraldistribution using the location and scale structure of the model. Slot param is filled accordingly with the argument trafo passed to L2LocationScaleFamily. In case L2derivDistr.0 is missing, L2derivDistr is computed via imageDistr, else L2derivDistr is assigned L2derivDistr.0, coerced to "UnivariateDistributionList". In case FisherInfo.0 is missing, Fisher information is computed from L2deriv using E. If distrSymm is missing, it is set to symmetry about loc. If L2derivSymm is missing, its location and scale components are set to no symmetry , respectively. if L2derivDistrSymm is missing, its location and scale components are set to no symmetry, respectively.

Value

Object of class "L2LocationScaleFamily"

Author(s)

Matthias Kohl [email protected],
Peter Ruckdeschel [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

L2LocationScaleFamily-class

Examples

F1 <- L2LocationScaleFamily()
plot(F1)

Description

Class of L2 differentiable parametric group families.

Objects from the Class

Objects can be created by calls of the form new("L2LocationScaleFamily", ...). More frequently they are created via the generating function L2LocationScaleFamily.

Slots

name

[inherited from class "ProbFamily"] object of class "character": name of the family.

distribution

[inherited from class "ProbFamily"] object of class "Distribution": member of the family.

distrSymm

[inherited from class "ProbFamily"] object of class "DistributionSymmetry": symmetry of distribution.

param

[inherited from class "ParamFamily"] object of class "ParamFamParameter": parameter of the family.

fam.call

[inherited from class "ParamFamily"] object of class "call": call by which parametric family was produced.

makeOKPar

[inherited from class "ParamFamily"] object of class "function": has argument param — the (total) parameter, returns valid parameter; used if optim resp. optimize— try to use “illegal” parameter values; then makeOKPar makes a valid parameter value out of the illegal one.

startPar

[inherited from class "ParamFamily"] object of class "function": has argument x — the data, returns starting parameter for optim resp. optimize— a starting estimator in case parameter is multivariate or a search interval in case parameter is univariate.

modifyParam

[inherited from class "ParamFamily"] object of class "function": mapping from the parameter space (represented by "param") to the distribution space (represented by "distribution").

props

[inherited from class "ProbFamily"] object of class "character": properties of the family.

L2deriv

[inherited from class "L2ParamFamily"] object of class "EuclRandVariable": L2 derivative of the family.

L2deriv.fct

[inherited from class "L2ParamFamily"] object of class "function": mapping from the parameter space (argument param of class "ParamFamParameter") to a mapping from observation x to the value of the L2derivative; L2deriv.fct is then used from observation x to value of the L2derivative; L2deriv.fct is used by modifyModel to move the L2deriv according to a change in the parameter

L2derivSymm

[inherited from class "L2ParamFamily"] object of class "FunSymmList": symmetry of the maps included in L2deriv.

L2derivDistr

[inherited from class "L2ParamFamily"] object of class "UnivarDistrList": list which includes the distribution of L2deriv.

L2derivDistrSymm

[inherited from class "L2ParamFamily"] object of class "DistrSymmList": symmetry of the distributions included in L2derivDistr.

FisherInfo.fct

[inherited from class "L2ParamFamily"] object of class "function": mapping from the parameter space (argument param of class "ParamFamParameter") to the set of positive semidefinite matrices; FisherInfo.fct is used by modifyModel to move the Fisher information according to a change in the parameter

FisherInfo

[inherited from class "L2ParamFamily"] object of class "PosDefSymmMatrix": Fisher information of the family.

LogDeriv

[inherited from class "L2GroupParamFamily"] object of class "function": has argument x; the negative logarithmic derivative of the density of the model distribution at the "standard" parameter value.

locscalename

[inherited from class "L2LocationScaleUnion"] object of class "character": names of location and scale parameter

Extends

Class "L2LocationScaleUnion", directly.
Class "L2GroupParamFamily", by class "L2LocationScaleUnion".
Class "L2ParamFamily", by class "L2GroupParamFamily".
Class "ParamFamily", by class "L2ParamFamily".
Class "ProbFamily", by class "ParamFamily".

Methods

modifyModel

signature(model = "L2LocationScaleFamily", param = "ParamFamParameter"): moves the L2-location and scale family model to parameter param

Author(s)

Matthias Kohl [email protected],
Peter Ruckdeschel [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

L2LocationScaleFamily, ParamFamily-class

Examples

F1 <- new("L2LocationScaleFamily")
plot(F1)

Description

Generates an object of class "L2LocationScaleFamily" in the situation where location is main, scale nuisance parameter.

Usage

L2LocationUnknownScaleFamily(loc = 0, scale = 1, name, centraldistribution = Norm(),
                      locscalename = c("loc", "scale"), modParam, LogDeriv,  
                      L2derivDistr.0, FisherInfo.0, distrSymm, L2derivSymm, 
                      L2derivDistrSymm, trafo, .returnClsName = NULL)

Arguments

Details

If name is missing, the default “L2 location family with unknown scale (as nuisance)” is used. The function modParam is optional. If it is missing, it is constructed from centraldistribution using the location and scale structure of the model. Slot param is filled accordingly with the argument trafo passed to L2LocationUnknownScaleFamily. In case L2derivDistr.0 is missing, L2derivDistr is computed via imageDistr, else L2derivDistr is assigned L2derivDistr.0, coerced to "UnivariateDistributionList". In case FisherInfo.0 is missing, Fisher information is computed from L2deriv using E. If distrSymm is missing, it is set to symmetry about loc. If L2derivSymm is missing, its location and scale components are set to no symmetry, respectively. if L2derivDistrSymm is missing, its location and scale components are set to no symmetry, respectively.

Value

Object of class "L2LocationScaleFamily"

Author(s)

Peter Ruckdeschel [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

L2LocationScaleFamily-class

Examples

F1 <- L2LocationUnknownScaleFamily()
plot(F1)

Description

Generates an object of class "L2ParamFamily".

Usage

L2ParamFamily(name, distribution = Norm(), distrSymm, 
              main = main(param), nuisance = nuisance(param),
              fixed = fixed(param), trafo = trafo(param),
              param = ParamFamParameter(name = paste("Parameter of", name),  
                          main = main, nuisance = nuisance, 
                          fixed = fixed, trafo = trafo),
              props = character(0),
              startPar = NULL, makeOKPar = NULL,
              modifyParam = function(theta){ Norm(mean=theta) },
              L2deriv.fct = function(param) {force(theta <- param@main)
                           return(function(x) {x-theta})},
              L2derivSymm, L2derivDistr, L2derivDistrSymm, 
              FisherInfo.fct, FisherInfo = FisherInfo.fct(param),
              .returnClsName = NULL, .withMDE = TRUE)

Arguments

Details

If name is missing, the default “L2 differentiable parametric family of probability measures” is used. In case distrSymm is missing it is set to NoSymmetry(). If param is missing, the parameter is created via main, nuisance and trafo as described in ParamFamParameter. In case L2derivSymm is missing, it is filled with an object of class FunSymmList with entries NonSymmetric(). In case L2derivDistr is missing, it is computed via imageDistr. If L2derivDistrSymm is missing, it is set to an object of class DistrSymmList with entries NoSymmetry(). In case FisherInfo is missing, it is computed from L2deriv using E.

Value

Object of class "L2ParamFamily"

Author(s)

Matthias Kohl [email protected],
Peter Ruckdeschel [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

L2ParamFamily-class

Examples

F1 <- L2ParamFamily()
plot(F1)

Description

Class of L2 differentiable parametric families.

Details

In the E-methods, diagnostics on the involved integrations are available if argument diagnostic is TRUE. Then there is attribute diagnostic attached to the return value, which may be inspected and accessed through showDiagnostic and getDiagnostic.

Objects from the Class

Objects can be created by calls of the form new("L2ParamFamily", ...). More frequently they are created via the generating function L2ParamFamily.

Slots

name

[inherited from class "ProbFamily"] object of class "character": name of the family.

distribution

[inherited from class "ProbFamily"] object of class "Distribution": member of the family.

distrSymm

[inherited from class "ProbFamily"] object of class "DistributionSymmetry": symmetry of distribution.

param

[inherited from class "ParamFamily"] object of class "ParamFamParameter": parameter of the family.

fam.call

[inherited from class "ParamFamily"] object of class "call": call by which parametric family was produced.

makeOKPar

[inherited from class "ParamFamily"] object of class "function": has argument param — the (total) parameter, returns valid parameter; used if optim resp. optimize— try to use “illegal” parameter values; then makeOKPar makes a valid parameter value out of the illegal one.

startPar

[inherited from class "ParamFamily"] object of class "function": has argument x — the data, returns starting parameter for optim resp. optimize— a starting estimator in case parameter is multivariate or a search interval in case parameter is univariate.

modifyParam

[inherited from class "ParamFamily"] object of class "function": mapping from the parameter space (represented by "param") to the distribution space (represented by "distribution").

props

[inherited from class "ProbFamily"] object of class "character": properties of the family.

L2deriv

object of class "EuclRandVariable": L2 derivative of the family. Its map slot must contain a list of functions. Each function in this list must have just one argument x, which is vectorized, (i.e., callable for a vector-valued x), and has a one-dimensional, numeric return value.

L2deriv.fct

object of class "function": mapping from the parameter space (argument param of class "ParamFamParameter") to a mapping from observation x to the value of the L2derivative; L2deriv.fct is then used from observation x to value of the L2derivative; L2deriv.fct is used by modifyModel to move the L2deriv according to a change in the parameter. More specifically, let us call the parts main and nuisance of the parameter the unknown parameter. If this unknown parameter is one-dimensional, the return value of L2deriv.fct must be a function in argument x, which is vectorized, (i.e., callable for a vector-valued x), and has a one-dimensional, numeric return value. In case the dimension of the unknown parameter is larger than one, the return value must be a list of functions, each of which satisfies the conditions formulated for the case of a one-dimensional parameter of interest. The order of the components of this list is the same as the order of the parameter coordinates in main, followed by the ones in nuisance.

L2derivSymm

object of class "FunSymmList": symmetry of the maps contained in L2deriv; a list of symmetry properties of the same length as the return value of L2deriv.fct .

L2derivDistr

object of class "OptionalDistrListOrCall" (i.e., NULL or an object of class "DistrList" or the respective call to generate the latter object): if non-null and non-call, a list which includes the distribution of L2deriv; the length of this list of univariate distributions must be of the same length as the return value of L2deriv.fct .

L2derivDistrSymm

object of class "DistrSymmList": symmetry of the distributions contained in L2derivDistr; the length of this list of symmetry properties must be of the same length as the return value of L2deriv.fct .

FisherInfo.fct

object of class "function": mapping from the parameter space (argument param of class "ParamFamParameter") to the set of positive semidefinite matrices; FisherInfo.fct is used by modifyModel to move the Fisher information according to a change in the parameter

FisherInfo

object of class "PosDefSymmMatrix": Fisher information of the family.

.withEvalL2derivDistr

logical of length one: if TRUE slot L2derivDistr gets evaluated, otherwise it is only kept as call.

Extends

Class "ParamFamily", directly.
Class "ProbFamily", by class "ParamFamily".

Methods

L2deriv

signature(object = "L2ParamFamily"): accessor function for L2deriv.

L2deriv

signature(object = "L2ParamFamily", param = "ParamFamParameter"): returns the L2derivative at param, i.e. evaluates slot function L2deriv.fct at param.

L2derivSymm

signature(object = "L2ParamFamily"): accessor function for L2derivSymm.

L2derivDistr

signature(object = "L2ParamFamily"): accessor function for L2derivDistr.

L2derivDistrSymm

signature(object = "L2ParamFamily"): accessor function for L2derivDistrSymm.

FisherInfo

signature(object = "L2ParamFamily"): accessor function for FisherInfo.

FisherInfo

signature(object = "L2ParamFamily", param = "ParamFamParameter"): returns the Fisher Information at param, i.e. evaluates slot function FisherInfo.fct at param.

checkL2deriv

signature(object = "L2ParamFamily"): check centering of L2deriv and compute precision of Fisher information.

E

signature(object = "L2ParamFamily", fun = "EuclRandVariable", cond = "missing"): expectation of fun under the distribution of object.

E

signature(object = "L2ParamFamily", fun = "EuclRandMatrix", cond = "missing"): expectation of fun under the distribution of object.

E

signature(object = "L2ParamFamily", fun = "EuclRandVarList", cond = "missing"): expectation of fun under the distribution of object.

plot

signature(x = "L2ParamFamily"): plot of distribution and L2deriv. More precisely, this method has arguments plot(x, withSweave = getdistrOption("withSweave"), main = FALSE, inner = TRUE, sub = FALSE, col.inner = par("col.main"), cex.inner = 0.8, bmar = par("mar")[1], tmar = par("mar")[3], ..., mfColRow = TRUE, to.draw.arg = NULL, withSubst = TRUE) where

x

object of class "L2ParamFamily"

withSweave

logical: if TRUE (for working with Sweave) no extra device is opened and height/width are not set

main

logical: is a main title to be used? or
just as argument main in plot.default.

inner

logical: do panels have their own titles? or
character vector of / cast to length 'number of plotted panels' with the corresponding panel titles. For further information, see also plot and the description of argument main in plot.default.

sub

logical: is a sub-title to be used? or
just as argument sub in plot.default.

tmar

top margin – useful for non-standard main title sizes

bmar

bottom margin – useful for non-standard sub title sizes

cex.inner

magnification to be used for inner titles relative to the current setting of cex; as in par; can be a vector of length 2; in this case the first component is for the distribution panels, the second for the L2-derivative-panels.

col.inner

character or integer code; color for the inner title

mfColRow

shall default partition in panels be used — defaults to TRUE

to.draw.arg

Either NULL (default; everything is plotted) or a vector of either integers (the indices of the subplots to be drawn) or characters — the names of the subplots to be drawn: these names are to be chosen among c("d","p","q", dimnms) where dimnms is either the row names of the trafo matrix rownames(trafo(x@param)) or if the last expression is NULL a vector "dim<dimnr>", dimnr running through the number of rows of the trafo matrix.

withSubst

logical; if TRUE (default) pattern substitution for titles and lables is used; otherwise no substitution is used.

...

addtional arguments for plot — see plot, plot.default, plot.stepfun

If ... contains argument ylim, this may either be as in plot.default (i.e. a vector of length 2) or a vector of length 4, where the first two elements are the values for ylim in panels "d.c" and "d.d", and the last two elements are the values for ylim resp. xlim in panels "p", "p.c", "p.d" and "q", "q.c", "q.d". In all title and axis label arguments, if withSubst is TRUE, the following patterns are substituted:

"%C"

class of argument x

"%A"

deparsed argument x

"%D"

time/date-string when the plot was generated

In addition, argument ... may contain arguments panel.first, panel.last, i.e., hook expressions to be evaluated at the very beginning and at the very end of each panel (within the then valid coordinates). To be able to use these hooks for each panel individually, they may also be lists of expressions (of the same length as the number of panels and run through in the same order as the panels).

The return value of the plot methods is an S3 object of class c("plotInfo","DiagnInfo"), i.e., a list containing the information needed to produce the respective plot, which at a later stage could be used by different graphic engines (like, e.g. ggplot) to produce the plot in a different framework. A more detailed description will follow in a subsequent version.

modifyModel

signature(model = "L2ParamFamily", param = "ParamFamParameter"): moves the L2-parametric Family model to parameter param

Author(s)

Matthias Kohl [email protected],
Peter Ruckdeschel [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

L2ParamFamily, ParamFamily-class

Examples

F1 <- new("L2ParamFamily")
plot(F1)

## selection of subpanels for plotting
F2 <- L2LocationScaleFamily()
layout(matrix(c(1,2,3,3), nrow=2, byrow=TRUE))
plot(F2,mfColRow = FALSE,
     to.draw.arg=c("p","q","loc"))
plot(F2,mfColRow = FALSE, inner=list("empirical cdf","pseudo-inverse",
     "L2-deriv, loc.part"), to.draw.arg=c("p","q","loc"))

Description

Generates an object of class "L2ScaleFamily".

Usage

L2ScaleFamily(scale = 1, loc = 0,  name, centraldistribution = Norm(),
              locscalename = c("loc", "scale"), modParam, LogDeriv,  
              L2derivDistr.0, FisherInfo.0, distrSymm, L2derivSymm, 
              L2derivDistrSymm, trafo, .returnClsName = NULL)

Arguments

Details

If name is missing, the default “L2 scale family” is used. The function modParam is optional. If it is missing, it is constructed from centraldistribution using the scale structure of the model. Slot param is filled accordingly with the argument trafo passed to L2ScaleFamily. In case L2derivDistr.0 is missing, L2derivDistr is computed via imageDistr, else L2derivDistr is assigned L2derivDistr.0, coerced to "UnivariateDistributionList". In case FisherInfo.0 is missing, Fisher information is computed from L2deriv using E. If distrSymm is missing, it is set to symmetry about loc. If L2derivSymm is missing, it is set to no symmetry, and if L2derivDistrSymm is missing, it is set to no symmetry.

Value

Object of class "L2ScaleFamily"

Author(s)

Matthias Kohl [email protected],
Peter Ruckdeschel [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

L2ScaleFamily-class

Examples

F1 <- L2ScaleFamily()
plot(F1)

Description

Class of L2 differentiable parametric group families.

Objects from the Class

Objects can be created by calls of the form new("L2ScaleFamily", ...). More frequently they are created via the generating function L2ScaleFamily.

Slots

name

[inherited from class "ProbFamily"] object of class "character": name of the family.

distribution

[inherited from class "ProbFamily"] object of class "Distribution": member of the family.

distrSymm

[inherited from class "ProbFamily"] object of class "DistributionSymmetry": symmetry of distribution.

param

[inherited from class "ParamFamily"] object of class "ParamFamParameter": parameter of the family.

fam.call

[inherited from class "ParamFamily"] object of class "call": call by which parametric family was produced.

makeOKPar

[inherited from class "ParamFamily"] object of class "function": has argument param — the (total) parameter, returns valid parameter; used if optim resp. optimize— try to use “illegal” parameter values; then makeOKPar makes a valid parameter value out of the illegal one.

startPar

[inherited from class "ParamFamily"] object of class "function": has argument x — the data, returns starting parameter for optim resp. optimize— a starting estimator in case parameter is multivariate or a search interval in case parameter is univariate.

modifyParam

[inherited from class "ParamFamily"] object of class "function": mapping from the parameter space (represented by "param") to the distribution space (represented by "distribution").

props

[inherited from class "ProbFamily"] object of class "character": properties of the family.

L2deriv

[inherited from class "L2ParamFamily"] object of class "EuclRandVariable": L2 derivative of the family.

L2deriv.fct

[inherited from class "L2ParamFamily"] object of class "function": mapping from the parameter space (argument param of class "ParamFamParameter") to a mapping from observation x to the value of the L2derivative; L2deriv.fct is then used from observation x to value of the L2derivative; L2deriv.fct is used by modifyModel to move the L2deriv according to a change in the parameter

L2derivSymm

[inherited from class "L2ParamFamily"] object of class "FunSymmList": symmetry of the maps included in L2deriv.

L2derivDistr

[inherited from class "L2ParamFamily"] object of class "UnivarDistrList": list which includes the distribution of L2deriv.

L2derivDistrSymm

[inherited from class "L2ParamFamily"] object of class "DistrSymmList": symmetry of the distributions included in L2derivDistr.

FisherInfo.fct

[inherited from class "L2ParamFamily"] object of class "function": mapping from the parameter space (argument param of class "ParamFamParameter") to the set of positive semidefinite matrices; FisherInfo.fct is used by modifyModel to move the Fisher information according to a change in the parameter

FisherInfo

[inherited from class "L2ParamFamily"] object of class "PosDefSymmMatrix": Fisher information of the family.

LogDeriv

[inherited from class "L2GroupParamFamily"] object of class "function": has argument x; the negative logarithmic derivative of the density of the model distribution at the "standard" parameter value.

locscalename

[inherited from class "L2LocationScaleUnion"] object of class "character": names of location and scale parameter

Extends

Class "L2LocationScaleUnion", directly.
Class "L2GroupParamFamily", by class "L2LocationScaleUnion".
Class "L2ParamFamily", by class "L2GroupParamFamily".
Class "ParamFamily", by class "L2ParamFamily".
Class "ProbFamily", by class "ParamFamily".

Methods

modifyModel

signature(model = "L2ScaleFamily", param = "ParamFamParameter"): moves the L2-scale family model to parameter param

Author(s)

Matthias Kohl [email protected],
Peter Ruckdeschel [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

L2ScaleFamily, ParamFamily-class

Examples

F1 <- new("L2ScaleFamily")
plot(F1)

Description

Generates an object of class "L2LocationScaleFamily" in the situation where scale is main, location nuisance parameter.

Usage

L2ScaleUnknownLocationFamily(loc = 0, scale = 1, name, centraldistribution = Norm(),
                      locscalename = c("loc", "scale"), modParam, LogDeriv,  
                      L2derivDistr.0, FisherInfo.0, distrSymm, L2derivSymm, 
                      L2derivDistrSymm, trafo, .returnClsName = NULL)

Arguments

Details

If name is missing, the default “L2 scale family with unknown location (as nuisance)” is used. The function modParam is optional. If it is missing, it is constructed from centraldistribution using the location and scale structure of the model. Slot param is filled accordingly with the argument trafo passed to L2ScaleUnknownLocationFamily. In case L2derivDistr.0 is missing, L2derivDistr is computed via imageDistr, else L2derivDistr is assigned L2derivDistr.0, coerced to "UnivariateDistributionList". In case FisherInfo.0 is missing, Fisher information is computed from L2deriv using E. If distrSymm is missing, it is set to symmetry about loc. If L2derivSymm is missing, its location and scale components are set to no symmetry, respectively. if L2derivDistrSymm is missing, its location and scale components are set to no symmetry, respectively.

Value

Object of class "L2LocationScaleFamily"

Author(s)

Peter Ruckdeschel [email protected]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

L2LocationScaleFamily-class

Examples

F1 <- L2ScaleUnknownLocationFamily()
plot(F1)

Description

Generates an object of class "L2ScaleFamily" which represents a lognormal scale family.

Usage

LnormScaleFamily(meanlog = 0, sdlog = 1, trafo)

Arguments

Details

The slots of the corresponding L2 differentiable parameteric family are filled.

Value

Object of class "L2ScaleFamily"

Author(s)

Matthias Kohl [email protected]

References

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

L2ParamFamily-class, Lnorm-class

Examples

(L1 <- LnormScaleFamily())
plot(L1)
Map(L2deriv(L1)[[1]])
checkL2deriv(L1)

Description

Generates an object of class "L2LocationScaleFamily" which represents a normal location and scale family.

Usage

LogisticLocationScaleFamily(location = 0, scale = 1, trafo)
LOGISTINT2

Arguments

Details

The slots of the corresponding L2 differentiable parameteric family are filled. LOGISTINT2 is a constant used for the scale part of the Fisher information. More precisely LOGISTINT2 equals to $\int_{-\infty}^{\infty} (\tanh(x/2)\,x-1)^2\,{\rm dlogis}(x)\,dx$.

Value

Object of class "L2LocationScaleFamily"

Author(s)

Peter Ruckdeschel [email protected]

References

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

L2ParamFamily-class, Logis-class

Examples

(L1 <- LogisticLocationScaleFamily())
## synonymous: L1 <- LogisticFamily()
plot(L1)
FisherInfo(L1)
### need smaller integration range:
distrExoptions("ElowerTruncQuantile"=1e-4,"EupperTruncQuantile"=1e-4)
checkL2deriv(L1)
distrExoptions("ElowerTruncQuantile"=1e-7,"EupperTruncQuantile"=1e-7)
##
set.seed(123)
x <- rlogis(100,location=1,scale=2)
CvMMDEstimator(x, L1)

Description

Methods for functions mceCalc and mleCalc in package distrMod;

Usage

mceCalc(x, PFam, ...)
mleCalc(x, PFam, ...)
## S4 method for signature 'numeric,ParamFamily'
mceCalc(x, PFam, criterion, 
                   startPar = NULL, penalty = 1e20, crit.name,
                   Infos = NULL, validity.check = TRUE,
                   withthetaPar = FALSE,...)
## S4 method for signature 'numeric,ParamFamily'
mleCalc(x, PFam, startPar = NULL, 
                   penalty = 1e20, dropZeroDensity = TRUE, Infos = NULL,
                    validity.check = TRUE, ...)
## S4 method for signature 'numeric,BinomFamily'
mleCalc(x, PFam, ...)
## S4 method for signature 'numeric,PoisFamily'
mleCalc(x, PFam, ...)
## S4 method for signature 'numeric,NormLocationFamily'
mleCalc(x, PFam, ...)
## S4 method for signature 'numeric,NormScaleFamily'
mleCalc(x, PFam, ...)
## S4 method for signature 'numeric,NormLocationScaleFamily'
mleCalc(x, PFam, ...)

Arguments

Details

mceCalc is used internally by function MCEstimator to allow for method dispatch according to argument PFam; similarly, and for the same purpose mleCalc is used internally by function MLEstimator. This way we / or any other developper can write particular methods for special cases where we may avoid using numerical optimization without interfering with existing code. For programming one's own mleCalc / mceCalc methods, there is the helper function meRes to produce consistent return values.

Value

a list with components

Description

Class of minimum criterion estimates.

Objects from the Class

Objects can be created by calls of the form new("MCEstimate", ...). More frequently they are created via the generating functions MCEstimator, MDEstimator or MLEstimator. More specifically, MDEstimator, CvMMDEstimator, and MLEstimator return objects of classes MDEstimate, CvMMDEstimate, and MLEstimate respectively, which each are immediate subclasses of MCEstimate (without further slots, for internal use in method dispatch).

Slots

name

Object of class "character": name of the estimator.

estimate

Object of class "ANY": estimate.

estimate.call

Object of class "call": call by which estimate was produced.

criterion

Object of class "numeric": minimum value of the considered criterion.

criterion.fct

Object of class "function": the considered criterion function; used for compatibility with class "mle" from package stats4; should be a function returning the criterion; i.e. a numeric of length 1 and should have as arguments all named components of argument untransformed.estimate

method

Object of class "character": the method by which the estimate was calculated, i.e.; "optim", "optimize", or "explicit calculation"; used for compatibility with class "mle" from package stats4, could be any character value.

Infos

object of class "matrix" with two columns named method and message: additional informations.

optimwarn

object of class "character" warnings issued during optimization.

optimReturn

object of class "ANY" the return value of the optimizer (or NULL if, e.g., closed form solutions are used).

startPar

— object of class "ANY"; filled either with NULL (no starting value used) or with "numeric" — the value of the starting parameter.

asvar

object of class "OptionalMatrix" which may contain the asymptotic (co)variance of the estimator.

samplesize

object of class "numeric" — the samplesize at which the estimate was evaluated.

nuis.idx

object of class "OptionalNumeric": indices of estimate belonging to the nuisance part

fixed

object of class "OptionalNumeric": the fixed and known part of the parameter.

trafo

object of class "list": a list with components fct and mat (see below).

untransformed.estimate

Object of class "ANY": untransformed estimate.

untransformed.asvar

object of class "OptionalNumericOrMatrix" which may contain the asymptotic (co)variance of the untransformed estimator.

completecases

object of class "logical" — complete cases at which the estimate was evaluated.

startPar

object of class "ANY"; usually filled with argument startPar of generating function MCEstimator, MLEstimator, MDEstimator.