\HeaderA{CWCV}{C Wavelet Cross-validation}{CWCV}
\keyword{smooth}{CWCV}
\begin{Description}\relax
Two-fold wavelet shrinkage cross-validation (in C)
\end{Description}
\begin{Usage}
\begin{verbatim}
CWCV(ynoise, ll, x = 1:length(ynoise), filter.number = 10, family = 
        "DaubLeAsymm", thresh.type = "soft", tol = 0.01, verbose = 0, 
        plot.it = TRUE, interptype = "normal")

\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{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.
\item[\code{ll}] The primary resolution that you wish to assume. No wavelet coefficients that are on coarser scales than ll will be thresholded.
\item[\code{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.
\item[\code{filter.number}] This selects the smoothness of wavelet that you want to perform wavelet shrinkage by cross-validation.
\item[\code{family}] specifies the family of wavelets that you want to use. The options are "DaubExPhase" and "DaubLeAsymm".
\item[\code{thresh.type }] this option specifies the thresholding type which can be "hard" or "soft".
\item[\code{tol}] this specifies the convergence tolerance for the cross-validation optimization routine (a golden section search).
\item[\code{verbose}] Controls the printing of "informative" messages whilst the computations progress. Such messages are generally annoying so it is turned off by default
\item[\code{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.
\item[\code{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.
\end{ldescription}
\end{Arguments}
\begin{Details}\relax
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 \code{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). 

\bold{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 \code{\LinkA{threshold}{threshold}} function using the \code{policy="sure"} option.
\end{Details}
\begin{Value}
A list with the following components 

\begin{ldescription}
\item[\code{x}] This is just the x that was input. It gets passed through more or less for convenience for the user.
\item[\code{ynoise}] A copy of the input ynoise noisy data.
\item[\code{xvwr}] The cross-validated wavelet shrunk estimate.
\item[\code{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.) 
\item[\code{xvthresh}] The cross-validated threshold
\item[\code{xvdof}] The number of non-zero coefficients in the cross-validated shrunk wavelet object (which is not returned).
\item[\code{uvdof}] The number of non-zero coefficients in the universal threshold shrunk wavelet object (which also is not returned)
\item[\code{xkeep}] always returns NULL!
\item[\code{fkeep}] always returns NULL!
\end{ldescription}
\end{Value}
\begin{Section}{RELEASE}
Version 3.0 Copyright Guy Nason 1994
\end{Section}
\begin{Note}\relax
Plots of the universal and cross-validated shrunk estimates might be plotted if \code{plot.it=TRUE.}
\end{Note}
\begin{SeeAlso}\relax
\code{\LinkA{threshold}{threshold}}. \code{\LinkA{threshold.wd}{threshold.wd}}.
\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
#
# This function is best used via the policy="cv" option in
# the threshold.wd function.
# See examples there.
#
\end{ExampleCode}
\end{Examples}

