R: C Wavelet Cross-validation

CWCV {wavethresh} | R Documentation

## C Wavelet Cross-validation

### Description

Two-fold wavelet shrinkage cross-validation (in C)

### Usage

    CWCV(ynoise, ll, x = 1:length(ynoise), filter.number = 10, family =
    	"DaubLeAsymm", thresh.type = "soft", tol = 0.01,
    	maxits=500, verbose = 0,
    	plot.it = TRUE, interptype = "noise")

### 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.
`ll` | The primary resolution that you wish to assume. No wavelet coefficients that are on coarser scales than ll will be thresholded.
`x` | 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).
`maxits` | maximum number of iterations 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.
`interptype` | Can take two values noise or normal. This option controls how cross-validation compares the estimate formed by leaving out the data with the "left-out" data. If interptype="noise" then two noisy values are averaged to compare with the estimated curve in between, otherwise if interptype="normal" then the curve estimate is averaged either side of a noisy left-out point.

### Details

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 the methods proposed in Donoho and Johnstone, 1995 or Johnstone and Silverman, 1997 which can be carried out in WaveThresh using the `threshold` function using the `policy="sure"` option.

### Value

A list with the following components

`x` | This is just the x that was input. It gets passed through more or less for convenience for the user.
`ynoise` | A copy of the input ynoise noisy data.
`xvwr` | The cross-validated wavelet shrunk estimate.
`yuvtwr` | The universal thresholded version (note this is merely a starting point for the cross-validation algorithm. It should not be ta ken seriously as an estimate. In particular its estimate of variance is likely to be inflated.)
`xvthresh` | The cross-validated threshold
`xvdof` | The number of non-zero coefficients in the cross-validated shrunk wavelet object (which is not returned).
`uvdof` | The number of non-zero coefficients in the universal threshold shrunk wavelet object (which also is not returned)
`xkeep` | always returns NULL!
`fkeep` | always returns NULL!

### RELEASE

Version 3.0 Copyright Guy Nason 1994

### Note

Plots of the universal and cross-validated shrunk estimates might be plotted if `plot.it=TRUE.`

### Author(s)

G P Nason

### See Also

`threshold`. `threshold.wd`.

### Examples

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

[Package wavethresh version 4.6.8 Index]