| Title: | Estimating Non-Simplified Vine Copulas Using Penalized Splines |
|---|---|
| Description: | Estimating Non-Simplified Vine Copulas Using Penalized Splines. |
| Authors: | Christian Schellhase <[email protected]> |
| Maintainer: | Christian Schellhase <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 0.2 |
| Built: | 2024-11-20 06:30:57 UTC |
| Source: | CRAN |
Estimating Non-Simplified Vine Copulas Using Penalized Splines
| Package: | pencopulaCond |
| Type: | Package |
| Version: | 0.2 |
| Date: | 2017-05-31 |
| License: GPL (>= 2) LazyLoad: | yes |
Christian Schellhase <[email protected]>
Estimating Non-Simplified Vine Copulas Using Penalized Splines, Schellhase, C. and Spanhel, F. (2017), Statistics and Computing.
#Simulating from a three-dimensional frank copula with #kendell's tau equal to 0.25, sample size N.set=100. #Please enlarge N.set for further studies. #require(copula) #N.set<-100 #cop <- archmCopula(family = "frank", dim = 3, param =2.39) #parMarg<-list(list(min=0,max=1),list(min=0,max=1),list(min=0,max=1)) #distr.cop <- mvdc(cop, margins=rep("unif",3), paramMargins = parMarg,marginsIdentical=TRUE) #c.X <- rMvdc(mvdc=distr.cop, n=N.set) #Y <- punif(c.X) #vine.copula<-vine(Y,d=2,d2=2,D=4,D3=4,q=1,m=2,cores=1,lambda=c(10000,100))#Simulating from a three-dimensional frank copula with #kendell's tau equal to 0.25, sample size N.set=100. #Please enlarge N.set for further studies. #require(copula) #N.set<-100 #cop <- archmCopula(family = "frank", dim = 3, param =2.39) #parMarg<-list(list(min=0,max=1),list(min=0,max=1),list(min=0,max=1)) #distr.cop <- mvdc(cop, margins=rep("unif",3), paramMargins = parMarg,marginsIdentical=TRUE) #c.X <- rMvdc(mvdc=distr.cop, n=N.set) #Y <- punif(c.X) #vine.copula<-vine(Y,d=2,d2=2,D=4,D3=4,q=1,m=2,cores=1,lambda=c(10000,100))
Calculating the density of the estimated Dvine at the point(s) val.
cal.Dvine(obj,val)cal.Dvine(obj,val)
obj |
object of class 'penDvine', result of 'Dvine'. |
val |
Values in which the current Dvine should be evaluated. |
The current Dvine is evaluated in val and the corresponding density values are returned.
The returing values are the density of the current Dvine at the point(s) 'val'.
Christian Schellhase <[email protected]>
Estimating Non-Simplified Vine Copulas Using Penalized Splines, Schellhase, C. and Spanhel, F. (2017), Statistics and Computing.
Calculating the density of the estimated regular vine at the point(s) val.
cal.vine(obj,val,cores)cal.vine(obj,val,cores)
obj |
Vine object of class 'pencopula'. |
val |
Values in which the current R-vine should be evaluated. |
cores |
Default=NULL, the number of cpu cores used for parallel computing can be specified. |
The current R-vine is evaluated in val and the corresponding density values are returned.
The returing values are the density of the current R-vine at the point(s) 'val'.
Christian Schellhase <[email protected]>
Estimating Non-Simplified Vine Copulas Using Penalized Splines, Schellhase, C. and Spanhel, F. (2017), Statistics and Computing.
Calculating the first derivative of the pencopula likelihood function w.r.t. parameter b.
Derv1(penden.env,temp.lam=FALSE,temp.ck=FALSE)Derv1(penden.env,temp.lam=FALSE,temp.ck=FALSE)
penden.env |
Containing all information, environment of pencopula(). |
temp.lam |
Calculating with temporal smoothing parameter lambda |
temp.ck |
Calculating with temporal weights ck of the spline basis functions |
Derv1.pen |
first order derivation of the penalized likelihood. |
Derv1.pen is saved in the environment.
Christian Schellhase <[email protected]>
Flexible Copula Density Estimation with Penalized Hierarchical B-Splines, Kauermann G., Schellhase C. and Ruppert, D. (2013), Scandinavian Journal of Statistics 40(4), 685-705.
Estimating Non-Simplified Vine Copulas Using Penalized Splines, Schellhase, C. and Spanhel, F. (2017), Statistics and Computing.
Calculating the second order derivative with and without penalty.
Derv2(penden.env, temp.lam = FALSE,temp.ck=FALSE,lam.fit=NULL)Derv2(penden.env, temp.lam = FALSE,temp.ck=FALSE,lam.fit=NULL)
penden.env |
Containing all information, environment of pendensity() |
temp.lam |
Calculating with temporal smoothing parameter lambda |
temp.ck |
Calculating with temporal weights ck of the spline basis functions |
lam.fit |
Indicating if the iterations for a new lambda are running |
We approximate the second order derivative in this approach with the negative fisher information.
Derv2.pen |
second order derivative w.r.t. beta with penalty |
Derv2.cal |
second order derivative w.r.t. beta without penalty. Needed for calculating of e.g. AIC. |
Derv2.cal and Derv2.pen are saved in the environment.
Christian Schellhase <[email protected]>
Flexible Copula Density Estimation with Penalized Hierarchical B-Splines, Kauermann G., Schellhase C. and Ruppert, D. (2013), Scandinavian Journal of Statistics 40(4), 685-705.
Estimating Non-Simplified Vine Copulas Using Penalized Splines, Schellhase, C. and Spanhel, F. (2017), Statistics and Computing.
These functions cooperate with each other for calculating the integral of the B-spline density basis. functions. 'distr.func.help' is the main program, calling 'poly.part', calculating the integral of the B-spline density basis in sections between neighbouring knots. 'distr.func.help' calculates analytical functions of the integral. Therefore the function 'poly.part' is needed to construct these functions.
distr.func.help(base,knots,penden.env,q,y,index) poly.part(i,j,knots,help.env,q, yi=NULL, poly=FALSE)distr.func.help(base,knots,penden.env,q,y,index) poly.part(i,j,knots,help.env,q, yi=NULL, poly=FALSE)
base |
values of the considered B-spline basis |
knots |
knots of the considered B-spline basis |
penden.env |
Containing all information, environment of pencopula() |
q |
degree of the B-Spline basis |
y |
data of the marginal B-spline basis |
index |
columns of the whole B-spline basis, each hierarchy level is integrated separately |
i |
internal values for calculating the polynomials of each B-Spline |
j |
internal values for calculating the polynomials of each B-Spline |
help.env |
internal environment of pencopula() for calculating the integral |
yi |
internal values for calculating the polynomials of each B-Spline |
poly |
internal value, TRUE/FALSE |
distr.func.help |
creating environment 'help.env', creating help points between each two neighbouring knots and calculates the integral each basis |
poly.part |
using in 'distr.func.help' for creating the polynomial functions of each interval of each two neighbouring knots |
Christian Schellhase <[email protected]>
Estimating Non-Simplified Vine Copulas Using Penalized Splines, Schellhase, C. and Spanhel, F. (2017), Statistics and Computing.
Calculating the actual fitted values of the response, depending on the actual parameter set b
f.hat.val(penden.env,cal=FALSE,temp=FALSE)f.hat.val(penden.env,cal=FALSE,temp=FALSE)
penden.env |
Containing all information, environment of pencopula() |
cal |
if TRUE, the final weights of one iteration are used for the calculation of the fitted values. |
temp |
if TRUE, the iteration for optimal weights is still in progress and the temporary weights are used for calculation of the fitted values. |
f.hat.val |
Fitted values for the current coefficents |
. f.hat.val is saved in the environment.
Christian Schellhase <[email protected]>
Flexible Copula Density Estimation with Penalized Hierarchical B-Splines, Kauermann G., Schellhase C. and Ruppert, D. (2013), Scandinavian Journal of Statistics 40(4), 685-705.
Estimating Non-Simplified Vine Copulas Using Penalized Splines, Schellhase, C. and Spanhel, F. (2017), Statistics and Computing.
Construction of the hierarchical B-spline density basis.
hierarch.bs(x, d, plot.bsp, typ, penden.env, int=FALSE)hierarch.bs(x, d, plot.bsp, typ, penden.env, int=FALSE)
x |
Marginal data for construction. |
d |
Hierarchy level of the marginal hierarchical B-spline density. |
plot.bsp |
Default = FALSE. If TRUE, each B-spline basis is plotted. |
typ |
typ==1 without open B-splines at the boundary typ==2 with open B-splines at the boundary. |
penden.env |
Containing all information, environment of pencopula(). |
int |
Default = FALSE. If TRUE, the integral of the hierarchical B-spline density basis is calculated (used for the distribution function of the estimation). |
First, the marginal hierarchical B-spline density basis is constructed for each covariate 'B.tilde'.
After the construction of each marginal basis, the hierarchical B-spline density basis is built in the main program pencopula(), using an object 'Index.basis.D' (saved in the environment). 'Index.basis.D' notes which compenent of the marginal basis has to be selected. In the main program the object 'tilde.Psi.d.D' is constructed. D refers to the maximum hierachy level and 'd' is the hierarchy level of the marginal hierarchical B-spline.
B.tilde |
'B.tilde' is the hierarchical B-spline density basis, returned by 'hierarch.bs'. |
int.B.tilde |
If 'int=TRUE', the integral of the hierachical B-spline density basis is calculated and returned by 'hierarch.bs'. |
Christian Schellhase <[email protected]>
Estimating Non-Simplified Vine Copulas Using Penalized Splines, Schellhase, C. and Spanhel, F. (2017), Statistics and Computing.
Calculating the equidistant knots for the estimation. Moreover, transformation of the knots are possible.
knots.start(penden.env) knots.transform(d,alpha = 0, symmetric = TRUE) knots.order(penden.env)knots.start(penden.env) knots.transform(d,alpha = 0, symmetric = TRUE) knots.order(penden.env)
penden.env |
Containing all information, environment of pencopula() |
d |
Hierarchy level of the marginal hierarchical B-spline basis. |
alpha |
Default = 0. Alpha is a tuning parameter, shifting the knots. |
symmetric |
Default = TRUE. If FALSE, the knots are selected without symmetry. |
'Knots.order' sorts the knots in the order, in which they disappear in the hierarchical B-spline basis.
knots |
Selected and sorted marginal knots for the estimation. |
knots.help |
Extended set of knots. It is needed for calculating the distribution function, help points for the integration of the B-spline density basis. |
k.order |
Order of the knots, corresponding to their order in the hierarchical B-spline density basis. |
knots.t |
The knots ordered with 'k.order' for further fucntions. |
tilde.Psi.knots.d |
Hierarchical B-Spline density basis for 'knots'. |
tilde.Psi.knots.d.help |
Hierarchical B-Spline density basis for 'knots.help'. |
All values are saved in the environment.
Christian Schellhase <[email protected]>
Flexible Copula Density Estimation with Penalized Hierarchical B-Splines, Kauermann G., Schellhase C. and Ruppert, D. (2013), Scandinavian Journal of Statistics 40(4), 685-705.
Estimating Non-Simplified Vine Copulas Using Penalized Splines, Schellhase, C. and Spanhel, F. (2017), Statistics and Computing.
Calculating the marginal likelihood of paircopula().
marg.likelihood(penden.env,pen.likelihood,temp=FALSE)marg.likelihood(penden.env,pen.likelihood,temp=FALSE)
penden.env |
Containing all information, environment of paircopula(). |
pen.likelihood |
Actual penalized likelihood for calculation, temporary or not. |
temp |
Default=FALSE, indicating if temporary values throughout iteration are calculated. |
marg.log.like |
Marginal log-likelihood, saved in the environment |
Christian Schellhase <[email protected]>
Estimating Non-Simplified Vine Copulas Using Penalized Splines, Schellhase, C. and Spanhel, F. (2017), Statistics and Computing.
'my.bspline' Integrates the normal B-Spline basis to a B-spline density basis. The dimension of the basis depends on the input of number of knots 'k' and of the order of the B-spline basis 'q'. 'int.my.bspline' is a function for transformation of open B-spline basis at the boundary to become a B-spline basis density.
my.bspline(h, q, knots, y, K, plot.bsp, typ) int.my.bspline(help.env)my.bspline(h, q, knots, y, K, plot.bsp, typ) int.my.bspline(help.env)
h |
if equidistant knots are used (default in pencopula()), h is the distance between two neighbouring knots |
q |
selected order of the B-spline basis |
knots |
selected values for the knots |
y |
values of the response variable |
K |
the number of knots for the construction of the base |
plot.bsp |
Indicator variable TRUE/FALSE if the integrated B-spline basis should be plotted |
typ |
typ==1 without open B-splines at the boundary typ==2 with open B-splines at the boundary |
help.env |
Internal environment of my.bspline(). |
Firstly, the function constructs the B-spline basis to the given number of knots 'K' and the given locations of the knots.
base.den |
The integrated B-Spline base of order q |
stand.num |
The coefficients for standardization of the ordinary B-Spline basis |
knots.val |
This return is a list. It consider of the used knots 'knots.val\$val', the help knots 'knots.val\$help' and the additional knots 'knots.val\$all', used for the construction of the base and the calculation of the distribution function of each B-Spline. |
K |
The transformed value of K, due to used order 'q' and the input of 'K' |
Christian Schellhase <[email protected]>
Flexible Copula Density Estimation with Penalized Hierarchical B-Splines, Kauermann G., Schellhase C. and Ruppert, D. (2013), Scandinavian Journal of Statistics 40(4), 685-705.
Estimating Non-Simplified Vine Copulas Using Penalized Splines, Schellhase, C. and Spanhel, F. (2017), Statistics and Computing.
Calculating the AIC-value and cAIC-value of the copula density estimation.
my.IC(penden.env,temp=FALSE)my.IC(penden.env,temp=FALSE)
penden.env |
Containing all information, environment of paircopula() |
temp |
Default=FALSE, if TRUE temporary values of AIC and cAIC are calculated. |
AIC is calculated as
cAIC is calculated as
BIC is calculated as
AIC |
sum of twice the negative non-penalized log likelihood and df(lambda) |
cAIC |
sum of twice the negative non-penalized log likelihood and df(lambda) and (2df(lambda)(df(lambda)+1))/(n-df(lambda)-1) |
BIC |
sum of twice the non-penalized log likelihood and log(n)*df(lambda) |
All values are saved in the environment.
Christian Schellhase <[email protected]>
Flexible Copula Density Estimation with Penalized Hierarchical B-Splines, Kauermann G., Schellhase C. and Ruppert, D. (2013), Scandinavian Journal of Statistics 40(4), 685-705.
Estimating Non-Simplified Vine Copulas Using Penalized Splines, Schellhase, C. and Spanhel, F. (2017), Statistics and Computing.
Calculating the optimal coefficients 'b' iteratively, using quadratic programing.
my.loop(penden.env)my.loop(penden.env)
penden.env |
Containing all information, environment of pencopula() |
'my.loop' optimates the log-likelihhod iteratively. Therefore, the routine checks the relative chance in the weights and stops the iteration, if the relative change of all weights 'b' is less than one percent. During the calculations of new weights 'b' in the routine 'new.weights', most of the values are called '.temp'. This add on unterlines the temporarily values. 'my.loop' checks the relative change in the weights. If the change is greater than one percent, the the real values are overwritten with the '.temp' values.
liste |
The results of each iteration are written in a matrix called 'liste', saved in the environment. 'liste' contains the penalized log-likelihood, the log-likelihood, 'lambda' and the weights 'b'. |
Christian Schellhase <[email protected]>
Estimating Non-Simplified Vine Copulas Using Penalized Splines, Schellhase, C. and Spanhel, F. (2017), Statistics and Computing.
Reverses a quadratic positive definite matrix.
my.positive.definite.solve(A, eps = 1e-15)my.positive.definite.solve(A, eps = 1e-15)
A |
quadratic positive definite matrix |
eps |
level of the lowest eigenvalue to consider |
The program makes an eigenvalue decomposition of the positive definite matrix A and searches all eigenvalues greater than eps. The value of return is the inverse matrix of A, constructed with the matrix product of the corresponding eigenvalues and eigenvectors.
The return is the inverse matrix of A.
Christian Schellhase <[email protected]>
Estimating Non-Simplified Vine Copulas Using Penalized Splines, Schellhase, C. and Spanhel, F. (2017), Statistics and Computing.
Calculating new weights b using quadratic programing.
new.weights(penden.env,start=FALSE)new.weights(penden.env,start=FALSE)
penden.env |
Containing all information, environment of pencopula() |
start |
Default=FALSE, for the first calculation some specifications are introduced. |
If the quadratic program does not find a new feasible solution, the whole program terminates. For solving the quadratic program, we use the function 'solve.QP' from the R-package 'quadprog'.
ck.val.temp |
Calculated new values for the weights 'b'. The add on 'temp' means, that there is a check in the next step if the weights 'b' have been converted or not. If converted, the new values 'ck.val.temp' are unnoted. If not converted, 'ck.val.temp' become the ordinary 'ck.val' for the next iteration. This check is done in my.loop. |
'ck.val.temp' is saved in the environment.
Christian Schellhase <[email protected]>
Flexible Copula Density Estimation with Penalized Hierarchical B-Splines, Kauermann G., Schellhase C. and Ruppert, D. (2013), Scandinavian Journal of Statistics 40(4), 685-705.
Estimating Non-Simplified Vine Copulas Using Penalized Splines, Schellhase, C. and Spanhel, F. (2017), Statistics and Computing.
Calculating the considered log likelihood.
pen.log.like(penden.env,cal=FALSE,temp.lam=FALSE,temp.ck=FALSE)pen.log.like(penden.env,cal=FALSE,temp.lam=FALSE,temp.ck=FALSE)
penden.env |
Containing all information, environment of pencopula() |
cal |
if TRUE, the final weights of one iteration are used for the calculation of the penalized log likelihood. |
temp.lam |
Calculating with temporal smoothing parameter lambda |
temp.ck |
Calculating with temporal weights ck of the spline basis functions |
The calculation depends on the estimated weights b, the penalized hierarchical B-splines Phi and the penalty paramters lambda.
pen.log.like |
Penalized log likelihood of the copula density. |
log.like |
Log-Likelihood of the copula density. |
The values are saved in the environment.
Christian Schellhase <[email protected]>
Flexible Copula Density Estimation with Penalized Hierarchical B-Splines, Kauermann G., Schellhase C. and Ruppert, D. (2013), Scandinavian Journal of Statistics 40(4), 685-705.
Estimating Non-Simplified Vine Copulas Using Penalized Splines, Schellhase, C. and Spanhel, F. (2017), Statistics and Computing.
Calculating the penalty matrix P depends on the number of covariates 'p', the order of differences to be penalized 'pen.order', the number of observations 'n' and the penalty parameters 'lambda”.
penalty.matrix(penden.env, temp = FALSE)penalty.matrix(penden.env, temp = FALSE)
penden.env |
Containing all information, environment of pencopula(). |
temp |
If TRUE, the iteration for a new 'b' is not finished and a temporary penalty matrix is calculated, default = FALSE. |
DDD.sum |
Penalty matrix P |
Matrix is saved in the environment.
Christian Schellhase <[email protected]>
Flexible Copula Density Estimation with Penalized Hierarchical B-Splines, Kauermann G., Schellhase C. and Ruppert, D. (2013), Scandinavian Journal of Statistics 40(4), 685-705.
Estimating Non-Simplified Vine Copulas Using Penalized Splines, Schellhase, C. and Spanhel, F. (2017), Statistics and Computing.
Calculating penalized (conditional) copula density with penalized hierarchical B-splines
pencopula(data,d=3,D=d,q=1,base="B-spline",max.iter=20,test.ind=FALSE, lambda=c(100,100),pen.order=2,data.frame=parent.frame(),cond=FALSE, fix.lambda=FALSE,id=NULL)pencopula(data,d=3,D=d,q=1,base="B-spline",max.iter=20,test.ind=FALSE, lambda=c(100,100),pen.order=2,data.frame=parent.frame(),cond=FALSE, fix.lambda=FALSE,id=NULL)
data |
'data' contains the data. 'data' has to be a matrix or a data.frame. The number of columns of 'data' is p. |
d |
refers to the hierachy level of the marginal hierarchical B-spline, default is d=3. |
D |
referes to the maximum hierachy level, default is D=3. If D<d, it follows D<-d. |
q |
degree of the marginal hierarchical B-spline. |
base |
By default, the used marginal basis is a 'B-spline'. Second possible option is 'Bernstein', using a Bernstein polynomial basis. |
max.iter |
maximum number of iteration, the default is max.iter=20. |
test.ind |
Default=FALSE. If test.ind=TRUE, the fitted log-likelihood of each pair-copula is evaluated. If ("log.like"/"n"<0.001), where "n" is the sample size, the program set the corresponding pair copula as independence copula. We do not use this in our simulations or applications in the article. |
lambda |
p-dimensional vector of penalty parameters, the values can be different. Default is lambda=c(100,100). |
pen.order |
The order of differences for the penalization, default is pen.order=2. |
data.frame |
reference to the data. Default reference is the parent.frame(). |
cond |
Determining if a conditional copula is estimated. Default=FALSE, only suitable for p=3. |
fix.lambda |
Default=FALSE, using the algorithm in the paper for estimating the optimal penalty parameter. If fix.lambda=TRUE, lambda is constant throughout the estimation. |
id |
Optional, one set id to any value. Especially important for simulations, starting with several starting values for lambda. |
Returning an object of class pencopula. The class pencopula consists of the environment 'penden.env', which includes all calculated values of the estimation approach. For a fast overview of the main results, one can use the function 'print.pencopula()'.
Christian Schellhase <[email protected]>
Flexible Copula Density Estimation with Penalized Hierarchical B-Splines, Kauermann G., Schellhase C. and Ruppert, D. (2013), Scandinavian Journal of Statistics 40(4), 685-705.
Estimating Non-Simplified Vine Copulas Using Penalized Splines, Schellhase, C. and Spanhel, F. (2017), Statistics and Computing.
Function 'pendenForm' interprets the input 'form' of the function pencopula(),transfers the data back to the main program.
pendenForm(penden.env)pendenForm(penden.env)
penden.env |
environment used in pendensity() |
Returning the values 'Y', the number of values 'n' and covariates 'p'.
Christian Schellhase <[email protected]>
Estimating Non-Simplified Vine Copulas Using Penalized Splines, Schellhase, C. and Spanhel, F. (2017), Statistics and Computing.
The function plots the estimated copula density or the copula distrubtion for a paircopula, using the R-package 'lattice'.
## S3 method for class 'pencopula' plot(x, val = NULL, marg = TRUE, plot = TRUE, int = FALSE, main.txt = NULL, sub.txt = NULL, contour = FALSE, cond = NULL, cuts = 20, cex = 1, cex.axes = 1, cex.contour=1, xlab = NULL, ylab = NULL, zlab=NULL, zlim=NULL, biv.margin=NULL, show.observ=FALSE,cond.cop=FALSE, cond.par,margin.normal=FALSE,...)## S3 method for class 'pencopula' plot(x, val = NULL, marg = TRUE, plot = TRUE, int = FALSE, main.txt = NULL, sub.txt = NULL, contour = FALSE, cond = NULL, cuts = 20, cex = 1, cex.axes = 1, cex.contour=1, xlab = NULL, ylab = NULL, zlab=NULL, zlim=NULL, biv.margin=NULL, show.observ=FALSE,cond.cop=FALSE, cond.par,margin.normal=FALSE,...)
x |
object of class 'pencopula'. |
val |
Default val = NULL, one can calculate the estimated density in for p-dimensional vector, e.g. val=c(0.5,1) for the two dimensional case. |
marg |
Default = TRUE, plotting the marginal densities. |
plot |
Default = TRUE, if 'FALSE' no plot is shown, e.g. for calculations with val != NULL. |
int |
Default = FALSE, if TRUE, the integral, i.e. the distribution of the copula density is plotted. |
main.txt |
Default = NULL shows 'd', 'D', the values of lambda, the penalty order and the degree of the B-splines. |
sub.txt |
Default = NULL shows the log-likelihood, the penalized log-likelihood and the AIC-value of the estimation. |
contour |
If TRUE, a contour plot is shown. Default = FALSE. |
cond |
Default = NULL, if the dimension of data 'p' is higher than 2, one can plot a two-dimensional conditional plot. The user specifies p-2 values for the plot, indicating with '-1'. So for a three-dimensional plot, cond=c(0,-1,-1) shows the density/distribution ith fixed first covariate and the second and third covariates vary. |
cuts |
Number of cuts for the contour plots, if contour=TRUE. |
cex |
Default = 1, determing the size of the main of the plot. |
cex.axes |
Default = 1, determing the size of the labels at the axes. |
cex.contour |
Default = 1, determing the size of the labels at the cuts of the contourplot. |
xlab |
Default = NULL and no text is printed at the xlab |
ylab |
Default = NULL and no text is printed at the ylab |
zlab |
Default = NULL and 'density' is printed at the zlab for int=FALSE and 'distribution' for int=TRUE. |
zlim |
For Default = NULL, the range of the estimated values determin zlim. Alternatively, one can suggest the range as a vector. |
biv.margin |
Determines for which parameter the bivariate marginal distribution/density is presented. |
show.observ |
Default = FALSE. If TRUE, plotting the original observation into a contourplot. For multivariate copulas the data corresponding to 'biv.margin' is plotted. Show.observ is not possible in combination with option 'cond'. |
cond.cop |
Default=FALSE. If cond.cop=TRUE, the object x have to be condtional copula - this option will disapper as the object itself contains this information. |
cond.par |
If cond.cop=TRUE, the plot is created for the conditioning argument cond.par |
margin.normal |
Default = FALSE. If TRUE, the plot is presented with margins following standard normal distribution. |
... |
further arguments |
For the two dimensional plots, a equidistant grid of 51 values between 0 and 1 is constructed. The plot consists of the density or distribution values in this grid points. For plots of high dimensional data (p>2), one has to fix p-2 covariates (see 'cond').
If 'val' is not NULL, the function returns a matrix with the calculated density or distribution values for the set 'val'.
Christian Schellhase <[email protected]>
Estimating Non-Simplified Vine Copulas Using Penalized Splines, Schellhase, C. and Spanhel, F. (2017), Statistics and Computing.
Printing the call of the estimation, the used basis, lambda and the corresponding values of AIC and BIC. Need an object of class pencopula.
## S3 method for class 'pencopula' print(x, ...)## S3 method for class 'pencopula' print(x, ...)
x |
x has to be object of class pencopula |
... |
further arguments |
Christian Schellhase <[email protected]>
Estimating Non-Simplified Vine Copulas Using Penalized Splines, Schellhase, C. and Spanhel, F. (2017), Statistics and Computing.
Estimating Non-Simplified Vine Copulas Using Penalized Splines
vine(data,d=2,d2=2,D=4,D3=6,lambda=c(100,50),type="Rvine",order.Dvine=FALSE,m=2, cores=NULL,q=1,mod.cond=TRUE,max.iter=51,fix.lambda=FALSE,RVM=NULL,cal.cond=FALSE, id=NULL,test.ind=FALSE,test.cond=2,lambda.search=FALSE,lam1.vec=NULL,lam2.vec=NULL)vine(data,d=2,d2=2,D=4,D3=6,lambda=c(100,50),type="Rvine",order.Dvine=FALSE,m=2, cores=NULL,q=1,mod.cond=TRUE,max.iter=51,fix.lambda=FALSE,RVM=NULL,cal.cond=FALSE, id=NULL,test.ind=FALSE,test.cond=2,lambda.search=FALSE,lam1.vec=NULL,lam2.vec=NULL)
data |
'data' contains the data. 'data' has to be a matrix or a data.frame with two columns. |
d |
refers to the hierachy level of the marginal hierarchical B-spline for copulas in the first tree of the vine, default is d=2. |
d2 |
refers to the hierachy level of the marginal hierarchical B-spline for copulas in the second tree and in the following trees of the vine, default is d2=2. |
D |
referes to the maximum hierachy level for copulas in the first tree of the vine, default is D=4. If D<d, it follows D<-d. |
D3 |
referes to the maximum hierachy level for copulas in the second tree and in the following trees of the vine, default is D3=6. |
lambda |
Starting values for lambda, first start values for copulas in the first tree, second start value for copulas in the second tree and in the following trees of the vine, default is lambda=c(100,50). |
type |
Default is type="Rvine", fitting a regular vine copula. An alternative is type="Dvine", fitting a D-vine copula. |
order.Dvine |
Only relevant for type="Dvine". Indicating if the first level of the Dvine is ordered, default order.Dvine=TRUE. |
m |
Indicating the order of differences to be penalised. Default is "m=2". |
cores |
Default=NULL, the number of cpu cores used for parallel computing can be specified. |
q |
Degree of B-splines. Default is q=1. |
mod.cond |
Default=TRUE. If mod.cond=FALSE each pair-copula in the vine is estimated as simplified copula. The argument test.cond varies the test for the simplyfing assumption, which is imported from the R-package pacotest. |
max.iter |
maximum number of iteration, the default is max.iter=51. |
fix.lambda |
Default=FALSE, using the algorithm in the paper for estimating the optimal penalty parameter. If fix.lambda=TRUE, lambda is constant throughout the estimation. |
RVM |
Default=NULL. If RVM is a RVine-Matrix, this matrix determines the structure of the vine. |
cal.cond |
Default=FALSE. If cal.cond=TRUE each copula in the second tree and in the following trees of the vine is estimated as conditional copula. |
id |
Optional, one set id to any value. Especially important for simulations, starting with several starting values for lambda. |
test.ind |
Default=FALSE. If test.ind=TRUE, the fitted log-likelihood of each pair-copula is evaluated. If ("log.like"/"n"<0.001), where "n" is the sample size, the program set the corresponding pair copula as independence copula. We do not use this in our simulations or applications in the article. |
test.cond |
If test.cond=2, testType='ECORR' is chosen for the test of the simplyfing assumption as proposed in the article. There is an additional second test available in the R-package pactotest. testType="VI" is chosen with test.cond=1. |
lambda.search |
TRUE/FALSE, indicating if a search about several starting values for lambda should be performed. If search is selected, the starting value 'lambda' does not work anymore. |
lam1.vec |
Vector of candidate values for penalty parameter lambda for copulas in the first tree of the vine |
.
lam2.vec |
Vector of candidate values for penalty parameter lambda for copulas in the second tree and in the following trees of the vine |
.
The calculation of the vine is done stepwise. The specifications in 'vine' are done for every paircopula in the vine with the identical specification. There is no option to change parameters for some pair-copulas.
Returning a list containing
vine |
The estimated vine copula, an object of class 'pencopulaCond' |
log.like |
the estimated log-likelihood |
log.like.vec |
A vector with the estimated log.like.vec of each pair-copula |
AIC |
AIC value |
AIC.vec |
A vector with the estimated AIC of each pair-copula |
cAIC |
corrected AIC value |
cAIC.vec |
A vector with the estimated cAIC of each pair-copula |
d |
Used d |
d2 |
Used d2 |
D |
Used D |
D3 |
Used D3 |
order |
the used order of the first level (reported only for D-vines) |
S |
Sequence seq(1:(dim(data)[2])) |
N |
Number of observations, that is dim(data)[1] |
base |
Used basis function |
q |
Used degree of the B-spline basis |
no.cond.dens |
Estimated number of condtional copulas |
pca |
Indicating the used number of pca |
D.struc |
Used D.struc |
type |
Selected type of the vine copula |
VineMatrix |
VineMatrix, reported for type="Rvine" |
Christian Schellhase <[email protected]>
Flexible Copula Density Estimation with Penalized Hierarchical B-Splines, Kauermann G., Schellhase C. and Ruppert, D. (2013), Scandinavian Journal of Statistics 40(4), 685-705.
Estimating Non-Simplified Vine Copulas Using Penalized Splines, Schellhase, C. and Spanhel, F. (2017), Statistics and Computing.