cv |
|
‘Leave-out-Half’ Cross-Validation |
DESCRIPTION
‘Leave-out-hal’ cross-validation strategy needed by the recanscombe, recanscombeTI, recfisz and recfiszTI procedures.
USAGE
M = cv(thr,x,L,h, type)
REQUIRED ARGUMENTS |
||
|
|
|
thr |
|
Threshold |
x |
|
1-d Noisy signal, length(signal)= 2^J |
L |
|
Coarsest resolution level |
h |
|
Quadrature mirror filter for wavelet transform |
type |
|
'Hard' for hard thresholding, 'Soft' for soft thresholding |
|
|
|
VALUE |
||
|
|
|
M |
|
Estimated mean integrated squared error |
BACKGROUND
The approach to cross-validation in wavelet regression was adopted by Nason (1996) to choose the threshold level thr. In order to directly apply the DWT, the author suggests breaking the original data set into 2 subsets of equal size: one containing only the even-indexed data, and the other, the odd-indexed data. The odd-indexed data will be used to "predict" the even-indexed data, and vice-versa, leading to a "leave-out-half" strategy. The estimate for the mean integrated squared error compares the interpolated wavelet estimators and the left out points and leads to an appropriate threshold value which is finally corrected since ones is using n/2 points instead of n.
REFERENCES
Nason, G.P. (1996).Wavelet shrinkage using cross-validation. J. R. Statist. Soc. B, 58, 463-479.
ACKNOWLEDGEMENT
The cv function is based on an Splus routine kindly provided by Guy Nason, and a MatLab routine kindly provided by Anestis Antoniadis, Jeremie Bigot and Theofanis Sapatinas.
SEE ALSO