| Title: | Haar-Fisz Functions for Binomial Data |
|---|---|
| Description: | Binomial Haar-Fisz transforms for Gaussianization as in Nunes and Nason (2009). |
| Authors: | Matt Nunes <[email protected]> |
| Maintainer: | Matt Nunes <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 1.0-3 |
| Built: | 2024-11-10 06:28:01 UTC |
| Source: | CRAN |
Samples binomial Fisz and Anscombe transformed random variables on a grid of binomial probabilities.
afgen(xgrid = seq(0, 1, length = 21), ygrid = seq(0, 1, length = 21), samples = 1000, binsize = 32)afgen(xgrid = seq(0, 1, length = 21), ygrid = seq(0, 1, length = 21), samples = 1000, binsize = 32)
xgrid |
vector of x co-ordinate probabilities. |
ygrid |
vector of x co-ordinate probabilities. |
samples |
the number of samples to draw from each random variable. |
binsize |
the binomial size of the binomial random variables. |
The function produces sampled values from the random variable:,
where are Bin(binsize,) random variables, for all combinations of values of in xgrid and in ygrid.
For Anscombe's transformation,
, the values correspond to the random variable with the larger binomial probability.
a |
an array of dimensions |
b |
an array of dimensions |
Matt Nunes ([email protected])
Anscombe, F.J. (1948) The transformation of poisson, binomial and negative binomial Data, Biometrika,35, 246–254.
Nunes, M. and Nason, G.P. (2009) A multiscale variance stabilization for binomial sequence proportion estimation. Statistica Sinica, 19
(1491–1510).
## varvalues<-afgen(xgrid=seq(0,1,length=21),ygrid=seq(0,1,length=21),samples=1000,binsize=32) ##creates 1000 samples of the two random variables zeta_B and A for each point ##(x,y) for x and y regularly-spaced probability vectors of length 21. #### varvalues<-afgen(xgrid=seq(0,1,length=21),ygrid=seq(0,1,length=21),samples=1000,binsize=32) ##creates 1000 samples of the two random variables zeta_B and A for each point ##(x,y) for x and y regularly-spaced probability vectors of length 21. ##
Does Anscombe's inverse sine transformation on a vector input.
ansc(x, binsize)ansc(x, binsize)
x |
input data vector |
binsize |
the binomial size corresponding to the observed binomial values. |
Performs the Anscombe calculation: .
y |
vector of transformed data corresponding to x. |
Matt Nunes ([email protected])
Anscombe, F.J. (1948) The transformation of poisson, binomial and negative binomial data. Biometrika, 35, 246-254.
afgen, hfdenoise, hfdenoise.wav, link{invansc}
#generate binomial data: x<-rbinom(100,10,.5) y<-ansc(x,10) #this is now the transformed data.#generate binomial data: x<-rbinom(100,10,.5) y<-ansc(x,10) #this is now the transformed data.
This function gives values for the asymptotic mean of the new binomial Fisz random variable for a grid of bivariate proportion values.
asymean(xgrid = seq(0, 1, length = 21), ygrid = seq(0, 1, length = 21), binsize = 32)asymean(xgrid = seq(0, 1, length = 21), ygrid = seq(0, 1, length = 21), binsize = 32)
xgrid |
vector of x co-ordinate probabilities. |
ygrid |
vector of y co-ordinate probabilities. |
binsize |
the binomial size of the binomial random variables. |
See afgen for an explanation of the computation.
zetam1m2 |
A matrix of dimension |
Matt Nunes ([email protected])
Fisz, M. (1955), The Limiting Distribution of a Function of Two Independent Random Variables and its Statistical Application, Colloquium Mathematicum, 3, 138–146.
means<-asymean(xgrid=seq(0,1,length=21),ygrid=seq(0,1,length=21),binsize=32) ## this produces a 21x21 matrix for an equally-spaced grid of binomial proportions.means<-asymean(xgrid=seq(0,1,length=21),ygrid=seq(0,1,length=21),binsize=32) ## this produces a 21x21 matrix for an equally-spaced grid of binomial proportions.
This function gives values for the asymptotic mean of the new binomial Fisz random variable.
asyvar(xgrid = seq(0, 1, length = 21), ygrid = seq(0, 1, length = 21))asyvar(xgrid = seq(0, 1, length = 21), ygrid = seq(0, 1, length = 21))
xgrid |
vector of x co-ordinate probabilities. |
ygrid |
vector of y co-ordinate probabilities. |
Due to the form of the asymptotic variance for equal binomial sizes, this does not need a specification of the binomial size
binsize (see asymean).
asyvar |
A matrix of dimension length(xgrid)xlength(ygrid) of values of the variance. |
Matt Nunes ([email protected])
Fisz, M. (1955), The Limiting Distribution of a Function of Two Independent Random Variables and its Statistical Application, Colloquium Mathematicum, 3, 138–146.
variance<-asyvar(xgrid=seq(0,1,length=21),ygrid=seq(0,1,length=21)) ## this produces a 21x21 matrix for an equally-spaced grid of binomial proportions.variance<-asyvar(xgrid=seq(0,1,length=21),ygrid=seq(0,1,length=21)) ## this produces a 21x21 matrix for an equally-spaced grid of binomial proportions.
Forward Haar-Fisz transform for binomial random variables.
binhf.wd(x, binsize = 1,print.info=FALSE)binhf.wd(x, binsize = 1,print.info=FALSE)
x |
data vector of binomial observations, of length a power of two. |
binsize |
the binomial size corresponding to x. |
print.info |
boolean to print some information about the coefficients. |
The procedure performs the Haar wavelet transform on the data x, and then modifies the wavelet coefficients by . The inverse Haar transform is then performed. This modification will stabilize the variance of the resulting vector.
l |
a list of two components transformed: transformed observations corresponding to x and cnew: scaling coefficient vector used in Fisz modification. This needs to be passed on to invbinhf.wd. |
Matt Nunes ([email protected])
Nunes, M.A. and Nason, G.P. (2009) A Multiscale Variance Stabilization for binomial sequence proportion estimation, Statistica Sinica, 19(4), 1491-1510.
x<-rbinom(256,32,.35) y<-binhf.wd(x,32)x<-rbinom(256,32,.35) y<-binhf.wd(x,32)
An example Bernoulli proportion function.
Blocks(x)Blocks(x)
x |
a sequence of ‘time points’ as input into the function. |
A proportion function based on the blocks function of Donoho, or that of Antoniadis and LeBlanc (2000). The extra “r" versions of these functions are reflected at the right endpoint.
y |
a vector of function values for the proportion function, corresponding to x. |
Matt Nunes ([email protected])
Antoniadis, A. and LeBlanc, F. (2000) Nonparametric wavelet regression for binary response. Statistics, 34, 183–213.
t<-seq(0,1,length=256) y<-Blocks(t) plot(t,y, type="l")t<-seq(0,1,length=256) y<-Blocks(t) plot(t,y, type="l")
Example DNA sequences.
data(chr20)data(chr20)
The datasets are the chromosome 20 sequence of the human genome, and the mhc dataset available from the Human Genome Project website, binary-coded by base pair content and curtailed to a power of two.
Modified EbayesThresh functions.
For help on these function, see the original help file supplied with the WaveThresh package. There is a modification to try and avoid zero noise standard deviation estimation.
Does Freeman-Tukey average inverse sine transformation on a vector input.
free(x, n)free(x, n)
x |
input data vector |
n |
the binomial size corresponding to the observed binomial values. |
a |
vector of transformed data corresponding to x. |
Matt Nunes ([email protected])
Freeman, M. F. and Tukey, J. W. (1950) Transformations related to the angular and the square root. Ann. Math. Stat., 21, 607–611.
#generate binomial data: x<-rbinom(100,10,.5) y<-free(x,10) #this is now the transformed data.#generate binomial data: x<-rbinom(100,10,.5) y<-free(x,10) #this is now the transformed data.
Does the inverse of the Freeman-Tukey inverse sine transformation on a vector input.
freeinv(y, n)freeinv(y, n)
y |
input data vector. |
n |
the binomial size corresponding to the observed binomial values. |
a |
vector of transformed data corresponding to y. |
Matt Nunes ([email protected])
Freeman, M. F. and Tukey, J. W. (1950) Transformations related to the angular and the square root. Ann. Math. Stat., 21, 607–611.
#generate binomial data: x<-rbinom(100,10,.5) y<-free(x,10) x1<-freeinv(y,10) #this should be the original data.#generate binomial data: x<-rbinom(100,10,.5) y<-free(x,10) x1<-freeinv(y,10) #this should be the original data.
Inverse Haar-NN transform for binomial random variables ("in-place").
hf.inv2(data, binsize = 1)hf.inv2(data, binsize = 1)
data |
data vector of binomial observations, of length a power of two. |
binsize |
the binomial size corresponding to x. |
The procedure performs the inverse "in-place" Haar-NN wavelet transform on the data x.
Matt Nunes ([email protected])
Nunes, M.A. and Nason, G.P. (2009) A Multiscale Variance Stabilization for binomial sequence proportion estimation, Statistica Sinica,19 (4), 1491–1510.
Proportion estimation procedure for simulations.
hfdenoise(n = 256, proportion = P2, binsize = 1, thrule = "ebayesthresh", van = 8, fam = "DaubLeAsymm", pl = 3, prior = "laplace", vscale = "independent", plotstep = FALSE, truncate = FALSE, ...)hfdenoise(n = 256, proportion = P2, binsize = 1, thrule = "ebayesthresh", van = 8, fam = "DaubLeAsymm", pl = 3, prior = "laplace", vscale = "independent", plotstep = FALSE, truncate = FALSE, ...)
n |
Length of vector to be sampled. |
proportion |
The function name of the proportion to be sampled. |
binsize |
The binomial size corresponding to the mean function proportion. |
thrule |
Thresholding procedure to be used in the smoothing. Possible values are "sureshrink" and "ebayesthresh". |
van |
the vanishing moments of the decomposing wavelet basis. |
fam |
the wavelet family to be used for the decomposing transform.Possible values are "DaubLeAsymm" and "DaubExPhase". |
pl |
the primary resolution to be used in the wavelet transform. |
prior |
Prior to be used in ebayesthresh thresholding. |
vscale |
argument to ebayesthresh thresholding procedure (variance calculation: "independent" or "bylevel"). |
plotstep |
Should all steps be plotted in estimation procedure? |
truncate |
Should the estimates be truncated to lie in [0,1]? |
... |
Any other optional arguments. |
This function creates a regularly-spaced vector on the unit interval of length length, and uses these values to create corresponding values using the proportion function. These values are then used as binomial probabilities to sample "observed" binomial random variables. The observation vector is then denoised using a wavelet transform defined by the arguments pl, van, fam with thresholding method thrule. This denoising is done for both Anscombe and the Haar-Fisz method for binomial random variables. The procedure is repeated times times, and the resulting proportion estimates averaged.
x |
regular grid on which the proportion function is evaluated. |
truep |
vector corresponding to x of proportion function values. |
fhat |
Binomial Haar-Fisz estimate. |
fhata |
Anscombe inverse sine estimate. |
fhatf |
Freeman-Tukey average inverse sine estimate. |
fl1 |
lokern estimate using binhf.wd as a preprocessor. |
fl2 |
lokern estimate using Anscombe as a preprocessor. |
bbwd |
wd object of binomial Haar-Fisz before thresholding. |
awd |
wd object of Anscombe before thresholding. |
b |
data from which estimates were computed (sampled from truep. |
bb |
data after being preprocessed with binomial Haar-Fisz. |
thr |
Thresholded wd object of bbwd. |
tmp |
Thresholded (binomial Haar-Fisz) data before postprocessing. |
Matt Nunes ([email protected])
sim<-hfdenoise() plot(sim$x,sim$truep,type="l", xlab="",ylab="Binomial Proportion") ##^^ shows original proportion to estimate. lines(sim$x,sim$fhat,col=2) lines(sim$x,sim$fhata,col=3) ##^^shows the estimates of the proportion from the two transforms.sim<-hfdenoise() plot(sim$x,sim$truep,type="l", xlab="",ylab="Binomial Proportion") ##^^ shows original proportion to estimate. lines(sim$x,sim$fhat,col=2) lines(sim$x,sim$fhata,col=3) ##^^shows the estimates of the proportion from the two transforms.
Denoise algorithm for thresholding methods supplied with wavethresh.
hfdenoise.wav(x, binsize, transform = "binhf", meth = "u", van = 1, fam = "DaubExPhase", min.level = 3,coarse=FALSE)hfdenoise.wav(x, binsize, transform = "binhf", meth = "u", van = 1, fam = "DaubExPhase", min.level = 3,coarse=FALSE)
x |
vector of observed values, of length a power of two. |
binsize |
the binomial size of the observed values x. |
transform |
A Gaussianizing transform. Possible values are "binhf" or "ansc". |
meth |
A wavelet thresholding method. Possible values are "u" for universal thresholding, or "c" for cross-validation. |
van |
the number of vanishing moments of the wavelet used in the wavelet denoiser. |
fam |
the wavelet family used in the wavelet denoiser. Possible values are "DaubLeAsymm" and "DaubExPhase". |
min.level |
the primary resolution level for the wavelet transform denoiser. |
coarse |
Boolean variable indicating whether a "coarsening" modification should be applied. For use with the chromosome datasets. |
The function pre and post-processes the observed data with either Anscombe's transform or the binomial Haar-Fisz transform, using a wavelet denoiser to smooth the data, specified by the inputs min.level, van and fam combined with the thresholding rule meth.If coarse is set to true, the first finest 11 coefficient levels are set to zero, corresponding to coefficients produced from = 2048 nucleotide bases.
fhat |
vector corresponding to x of the estimated binomial proportion. |
This function requires the package wavethresh.
Matt Nunes ([email protected])
library(wavethresh) #create a sample intensity vector: int<-sinlog(seq(0,1,length=256)) x<-NULL for(i in 1:256){ x[i]<-rbinom(1,1,int[i]) } est<-hfdenoise.wav(x,1,transform="ansc","u",6,"DaubLeAsymm",3,FALSE)library(wavethresh) #create a sample intensity vector: int<-sinlog(seq(0,1,length=256)) x<-NULL for(i in 1:256){ x[i]<-rbinom(1,1,int[i]) } est<-hfdenoise.wav(x,1,transform="ansc","u",6,"DaubLeAsymm",3,FALSE)
Forward Haar transform.
ht(x)ht(x)
x |
data vector of (binomial) observations, of length a power of two. |
The procedure performs the Haar wavelet transform on the data x.
x<-rbinom(256,32,.35) ht(x)x<-rbinom(256,32,.35) ht(x)
Inverse Haar transform for binomial random variables.
ht.inv(data)ht.inv(data)
data |
transformed (binomial) observations: can be a list output from |
The procedure performs the inverse Haar wavelet transform.
res |
datapoints in the function domain. |
sm1 |
smooth coefficients during the inverse transform. |
Nunes, M.A. and Nason, G.P. (2009) A Multiscale Variance Stabilization for binomial sequence proportion estimation, Statistica Sinica,19 (4), 1491–1510.
x<-rbinom(256,32,.35) hx<-ht2(x) y<-ht.inv(x)x<-rbinom(256,32,.35) hx<-ht2(x) y<-ht.inv(x)
Does the inverse of Anscombe's inverse sine transformation on a vector input.
invansc(y, n)invansc(y, n)
y |
input data vector. |
n |
the binomial size corresponding to the observed binomial values. |
x |
vector of transformed data corresponding to y. |
Matt Nunes ([email protected])
Anscombe, F.J. (1948) The transformation of poisson, binomial and negative binomial data. Biometrika, 35, 246-254.
ansc, hfdenoise, hfdenoise.wav
#generate binomial data: x<-rbinom(100,10,.5) y<-ansc(x,10) x1<-invansc(y,10) #this should be the original data.#generate binomial data: x<-rbinom(100,10,.5) y<-ansc(x,10) x1<-invansc(y,10) #this should be the original data.
Performs the inverse Haar-NN transform for binomial random variables.
invbinhf.wd(transformed, binsize = 1,print.info=FALSE)invbinhf.wd(transformed, binsize = 1,print.info=FALSE)
transformed |
a list of two components transformed: transformed observations of length a power of two and cnew: scaling coefficient vector used in Fisz modification. |
binsize |
the binomial size corresponding to the vector transformed. |
print.info |
boolean to print some information about the coefficients. |
The procedure performs the Haar wavelet transform on the data transformed, and then modifies the wavelet coefficients by =*sqrt((N-)/2N). The inverse Haar transform is then performed. This modification will stabilize the variance of the resulting vector.
estimate |
a vector of transformed observations corresponding to transformed. |
This function requires the package wavethresh.
Matt Nunes ([email protected])
Nunes, M.A. and Nason, G.P. (2009) “A Multiscale Variance Stabilization for binomial sequence proportion estimation", Statistica Sinica,19 (4), 1491–1510.
x<-rbinom(256,32,.35) y<-binhf.wd(x,32) x1<-invbinhf.wd(y,32)x<-rbinom(256,32,.35) y<-binhf.wd(x,32) x1<-invbinhf.wd(y,32)
Calculates the root squared error of two vectors.
norm(x,y)norm(x,y)
x |
input data vector |
y |
input data vector |
e |
error between the two input vectors |
Matt Nunes ([email protected])
#generate data: x<-y<-runif(100) error<-norm(x,y) #this is the difference between the vectors.#generate data: x<-y<-runif(100) error<-norm(x,y) #this is the difference between the vectors.
An example binomial intensity vector.
data(pintens)data(pintens)
The format is: num [1:1024] 0.278 0.278 0.278 0.278 0.278 ...
The intensity is a vector of length 1024, based on a scaled ‘bumps’ function of Donoho and Johnstone.
data(pintens) plot(pintens,type="l")data(pintens) plot(pintens,type="l")
Plotting function for proportion estimates procedure.
plotest(l, plot.it = FALSE, verbose = FALSE)plotest(l, plot.it = FALSE, verbose = FALSE)
l |
A results list from doall. |
plot.it |
Should results be plotted? |
verbose |
Should extra information be given during the procedure? |
This function uses norm to compute errors for estimates produced by doall.
hfn |
error between Haar-Fisz estimate and truep of doall. |
an |
error between Anscombe estimate and truep of doall. |
fn |
error between Freeman-Tukey estimate and truep of doall. |
Matt Nunes ([email protected])
sim<-hfdenoise() plotest(sim)sim<-hfdenoise() plotest(sim)
Proportion estimation procedure for simulations.
propest.wav(proportion = P2, binsize=1,length = 256, times = 100, meth = "u", van = 6, fam = "DaubLeAsymm", min.level = 3)propest.wav(proportion = P2, binsize=1,length = 256, times = 100, meth = "u", van = 6, fam = "DaubLeAsymm", min.level = 3)
proportion |
A Bernoulli proportion/binomial mean function. Examples are P2, P4 and sinlog. |
binsize |
The binomial size corresponding to the mean function proportion. |
length |
Length of vector to be produced. Must be a power of two. |
times |
The number of times to sample the proportion. |
meth |
A wavelet thresholding method. Possible values are "u" for universal thresholding, or "c" for cross-validation. |
van |
the number of vanishing moments of the wavelet used in the wavelet denoiser. |
fam |
the wavelet family used in the wavelet denoiser. Possible values are "DaubLeAsymm" and "DaubExPhase". |
min.level |
the primary resolution level for the wavelet transform denoiser. |
This function creates a regularly-spaced vector on the unit interval of length length, and uses these values to create corresponding values using the proportion function. These values are then used as binomial probabilities to sample "observed" binomial random variables. The observation vector is then denoised using a wavelet transform defined by the arguments van, fam, min.level with thresholding method meth. This denoising is done for both Anscombe and the Haar-Fisz method for binomial random variables. The procedure is repeated times times, and the resulting proportion estimates averaged.
x |
regular grid on which the proportion function is evaluated. |
y |
vector corresponding to x of proportion function values. |
b |
matrix of dimensions timesxlength of sampled binomial variables. |
e |
matrix of dimensions timesxlength of estimated values of the proportion function, for the binomial Haar-Fisz transform. |
ea |
matrix of dimensions timesxlength of estimated values of the proportion function, for Anscombe's transform. |
meanfhat |
averaged proportion estimate for the binomial Haar-Fisz transform. |
meanfhata |
averaged proportion estimate for Anscombe's transform. |
amse |
average mean square error for the binomial Haar-Fisz transform. |
amsea |
average mean square error for Anscombe's transform. |
Matt Nunes ([email protected])
## Not run: sim<-propest.wav(proportion = P2, binsize=1,length = 256, times = 1000, meth = "u", van = 6, fam = "DaubLeAsymm", min.level = 4) plot(sim$x,sim$y,type="l",xlab="",ylab="Binomial mean function") ##^^ shows original proportion to estimate. lines(sim$x,sim$meanfhat,col=2) lines(sim$x,sim$meanfhata,col=3) ##^^shows the estimates of the proportion from the two transforms. ## End(Not run)## Not run: sim<-propest.wav(proportion = P2, binsize=1,length = 256, times = 1000, meth = "u", van = 6, fam = "DaubLeAsymm", min.level = 4) plot(sim$x,sim$y,type="l",xlab="",ylab="Binomial mean function") ##^^ shows original proportion to estimate. lines(sim$x,sim$meanfhat,col=2) lines(sim$x,sim$meanfhata,col=3) ##^^shows the estimates of the proportion from the two transforms. ## End(Not run)
A Q-Q value generator.
qqnormy(y)qqnormy(y)
y |
data sample |
This is an equivalent to qqnorm, but returning sorted values. See qqnorm.
y |
vector of quantile values. |
Matt Nunes ([email protected])
A function to generate Q-Q plots (from simulations) for the Anscombe and (binomial) Haar-Fisz transforms.
qqstuff(intensity, binsize = 4, paths = 100, respaths = 1000, plot.q = FALSE, plot.sq = FALSE)qqstuff(intensity, binsize = 4, paths = 100, respaths = 1000, plot.q = FALSE, plot.sq = FALSE)
intensity |
an Bernoulli intensity vector, e.g. pintens. |
binsize |
a binomial size to generate a binomial mean vector. |
paths |
the number of paths sampled from the mean vector to use in Q-Q calculations. |
respaths |
the number of residual paths to use in squared residual calculations. |
plot.q |
A boolean variable, indicating whether simulation Q-Q plots should be outputted or not. |
plot.sq |
A boolean variable, indicating whether simulation squared residual plots should be outputted or not. |
respaths paths are sampled from the mean intensity vector. From these, the first paths are used to generate Q-Q data, which are then averaged for the Q-Q plots. The original paths are used to calculate a squared residual vector corresponding to the mean intensity vector.
qqinfo. A 8 component list of quantile and residual plot information.
vmat |
A matrix of dimensions respathsxlength(intensity), each row being a path from the intensity vector. |
Av |
A matrix of dimensions respathsxlength(intensity), each row an Anscombe-transformed path. |
bfv |
A matrix of dimensions respathsxlength(intensity), each row a binomial Haar-Fisz-transformed path. |
vminusl |
A matrix of the difference between the paths and the mean intensity. |
vminusl |
A matrix of the difference between the Anscombe-transformed paths and the mean intensity. |
vminusl |
A matrix of the difference between the binomial Haar-Fisz-transformed paths and the mean intensity. |
Asqres |
vector of squared residuals of Anscombe-transformed paths. |
bfsqres |
vector of squared residuals of binomial Haar-Fisz-transformed paths. |
This function requires the package wavethresh. N.B. Since this function returns a lot of information, assign the output to a variable, to avoid printing endless information in the console.
Matt Nunes ([email protected])
data(pintens) a<-qqstuff(intensity=pintens,binsize=4,paths=100,respaths=100,plot.q=TRUE,plot.sq=TRUE) #plots some interesting graphs.data(pintens) a<-qqstuff(intensity=pintens,binsize=4,paths=100,respaths=100,plot.q=TRUE,plot.sq=TRUE) #plots some interesting graphs.
This function shifts a vector input a certain number of places in the direction desired.
shift(v, places, dir = "right")shift(v, places, dir = "right")
v |
a vector of input values. |
places |
the number of places to shift v. |
dir |
The direction to shift v. |
The function shifts the vector v by places in the direction of direction, using wrapping at the boundaries. Used for cycle spinning.
vnew |
the shifted version of v. |
Matt Nunes ([email protected])
v<-runif(10) #have a look at v: v #now shift the values 4 places to the right... shift(v,4,dir="right")v<-runif(10) #have a look at v: v #now shift the values 4 places to the right... shift(v,4,dir="right")
Proportion estimation procedure for simulations.
simsij(nsims = 100, n = 256, proportion = P2, binsize = 1, thrule = "ebayesthresh", van = 8, fam = "DaubLeAsymm", pl = 3, prior = "laplace", vscale = "independent", plotstep = FALSE, a = NA,truncate = FALSE, ...)simsij(nsims = 100, n = 256, proportion = P2, binsize = 1, thrule = "ebayesthresh", van = 8, fam = "DaubLeAsymm", pl = 3, prior = "laplace", vscale = "independent", plotstep = FALSE, a = NA,truncate = FALSE, ...)
nsims |
The number of times to repeat the function doall (on random datasets from proportion). |
n |
Length of vector to be sampled. |
proportion |
The function name of the proportion to be sampled. |
binsize |
The binomial size corresponding to the mean function proportion. |
thrule |
Thresholding procedure to be used in the smoothing. Possible values are "sureshrink" and "ebayesthresh". |
van |
the vanishing moments of the decomposing wavelet basis. |
fam |
the wavelet family to be used for the decomposing transform.Possible values are "DaubLeAsymm" and "DaubExPhase". |
pl |
the primary resolution to be used in the wavelet transform. |
prior |
Prior to be used in ebayesthresh thresholding. |
vscale |
argument to ebayesthresh thresholding procedure (variance calculation: "independent" or "bylevel"). |
plotstep |
Should all steps be plotted in estimation procedure? |
a |
the a argument for |
truncate |
Should the estimates be truncated to lie in [0,1]? |
... |
Any other optional arguments. |
This function creates a regularly-spaced vector on the unit interval of length length, and uses these values to create corresponding values using the proportion function. These values are then used as binomial probabilities to sample "observed" binomial random variables. The observation vector is then denoised using a wavelet transform defined by the arguments van, fam, min.level with thresholding method meth. This denoising is done for both Anscombe and the Haar-Fisz method for binomial random variables. The procedure is repeated times times, and the resulting proportion estimates averaged.
x |
regular grid on which the proportion function is evaluated. |
truep |
vector corresponding to x of proportion function values. |
ans |
matrix containing the errors from each of the nsims doall runs. |
est |
Array containing the nsims estimates produced by Anscombe and Haar-Fisz. |
bin |
Matrix of the raw binomial samples for each of the nsims runs. |
Matt Nunes ([email protected])
## Not run: a<-simsij(nsims=100) plot(a$est[1,,1]) ##^^ shows 1st binomial Haar-Fisz estimate. ## End(Not run)## Not run: a<-simsij(nsims=100) plot(a$est[1,,1]) ##^^ shows 1st binomial Haar-Fisz estimate. ## End(Not run)
This function generates useful simulation statistics for NN and Anscombe transforms.
statgen(valuelist, xgrid = seq(0, 1, length = 21), ygrid = seq(0, 1, length = 21), binsize = 32, plot.m = FALSE, plot.v = FALSE, plot.ks = FALSE, ptype = "persp")statgen(valuelist, xgrid = seq(0, 1, length = 21), ygrid = seq(0, 1, length = 21), binsize = 32, plot.m = FALSE, plot.v = FALSE, plot.ks = FALSE, ptype = "persp")
valuelist |
a two component list as produced by afgen. |
xgrid |
a vector of x coordinate binomial proportions. |
ygrid |
a vector of x coordinate binomial proportions. |
binsize |
binomial size to use in simulations. |
plot.m |
A boolean variable, indicating whether mean simulation plots should be outputted. |
plot.v |
A boolean variable, indicating whether variance simulation plots should be outputted. |
plot.ks |
A boolean variable, indicating whether Kolmogorov-Smirnov simulation plots should be outputted. |
ptype |
where appropriate, the type of plots to be produced. Possible values are "persp" for 3D persective plots or "contour" for corresponding contour plots. |
The function does several sample variance plots, Kolmogorov-Smirnov and mean plots for the data in the variable valuelist (for both Anscombe and binomial Haar-Fisz transforms).
afm |
matrix of sample mean values for binomial Haar-Fisz samples. |
anm |
matrix of sample mean values for Anscombe samples. |
afv |
matrix of sample variance values for binomial Haar-Fisz samples. |
anv |
matrix of sample variance values for Anscombe samples. |
afk |
matrix of Kolmogorov-Smirnof statistics for binomial Haar-Fisz samples. |
ank |
matrix of Kolmogorov-Smirnof statistics for Anscombe samples. |
Matt Nunes ([email protected])
a<-afgen(xgrid = seq(0, 1, length = 21), ygrid = seq(0, 1, length = 21), samples = 1000, binsize = 32) b<-statgen(a,xgrid=seq(0,1,length=21),ygrid=seq(0,1,length=21),binsize=32,plot.m=FALSE, plot.v=TRUE,plot.ks=FALSE,ptype="persp")a<-afgen(xgrid = seq(0, 1, length = 21), ygrid = seq(0, 1, length = 21), samples = 1000, binsize = 32) b<-statgen(a,xgrid=seq(0,1,length=21),ygrid=seq(0,1,length=21),binsize=32,plot.m=FALSE, plot.v=TRUE,plot.ks=FALSE,ptype="persp")