WaveletCV: Wavelet cross-validation

Description

Two-fold wavelet shrinkage cross-validation (there is a faster C based version CWCV.)

Usage

WaveletCV(ynoise, x = 1:length(ynoise), filter.number = 10, family = 
	"DaubLeAsymm", thresh.type = "soft", tol = 0.01, verbose = 0, 
	plot.it = TRUE, ll=3)

Arguments

ynoise

A vector of dyadic (power of two) length that contains the noisy data that you wish to apply wavelet shrinkage by cross-validation to.

This function is capable of producing informative plots. It can be useful to supply the x values corresponding to the ynoise values. Further this argument is returned by this function which can be useful for later processors.

filter.number

This selects the smoothness of wavelet that you want to perform wavelet shrinkage by cross-validation.

family

specifies the family of wavelets that you want to use. The options are "DaubExPhase" and "DaubLeAsymm".

thresh.type

this option specifies the thresholding type which can be "hard" or "soft".

tol

this specifies the convergence tolerance for the cross-validation optimization routine (a golden section search).

verbose

Controls the printing of "informative" messages whilst the computations progress. Such messages are generally annoying so it is turned off by default.

plot.it

If this is TRUE then plots of the universal threshold (used to obtain an upper bound on the cross-validation threshold) reconstruction and the resulting cross-validation estimate are produced.

The primary resolution that you wish to assume. No wavelet coefficients that are on coarser scales than ll will be thresholded.

Value

A list with the following components
xThis is just the x that was input. It gets passed through more or less for convenience for the user.
ynoiseA copy of the input ynoise noisy data.
xvwrThe cross-validated wavelet shrunk estimate.
yuvtwrThe universal thresholded version (note this is merely a starting point for the cross-validation algorithm. It should not be taken seriously as an estimate. In particular its estimate of variance is likely to be inflated.)
xvthreshThe cross-validated threshold
uvthreshThe universal threshold (again, don't take this value too seriously. You might get better performance using the threshold function directly with specialist options.
xvdofThe number of non-zero coefficients in the cross-validated shrunk wavelet object (which is not returned).
uvdofThe number of non-zero coefficients in the universal threshold shrunk wavelet object (which also is not returned)
xkeepalways returns NULL!
fkeepalways returns NULL!

Details

Note: a faster C based implementation of this function called CWCV is available. It takes the same arguments (although it has one extra minor argument) and returns the same values.

Compute the two-fold cross-validated wavelet shrunk estimate given the noisy data ynoise according to the description given in Nason, 1996.

You must specify a primary resolution given by ll. This must be specified individually on each data set and can itself be estimated using cross-validation (although I haven't written the code to do this).

Note. The two-fold cross-validation method performs very badly if the input data is correlated. In this case I would advise using other methods.

Examples

Run this code

#
# This function is best used via the policy="cv" option in
# the threshold.wd function.
# See examples there.
#

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