WaveThresh
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rsswav
DESCRIPTION
Compute mean of residual sum of squares (RSS) for odd prediction of
even ordinates and vice versa using wavelet shrinkage with a specified
threshold. This is a
component of the WaveletCV cross validation function.
A version implemented in C exists called Crsswav.
USAGE
rsswav(noisy, value = 1, filter.number = 10, family = "DaubLeAsymm",
thresh.type = "hard", ll = 3)
REQUIRED ARGUMENTS
- noisy
- A vector of dyadic (power of two) length that contains the noisy
data that you wish to compute the averaged RSS for.
OPTIONAL ARGUMENTS
- value
- The specified threshold.
- 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".
- ll
- 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
- ssq
- The RSS value that was computed
- df
- The dof value computed on the thresholded
wavelet transform of the data with the given threshold and
thresholding options. (Although this is not really used for anything).
- value
- The value argument that was specified.
- type
- the
thresh.type argument that was specified.
- lev
- The vector
ll:(nlevels(noisy)-1) (i.e. the levels
that were thresholded).
SIDE EFFECTS
None.
DETAILS
Note: a faster C based implementation of this
function called Crsswav is available. It takes
the same arguments and returns the same values.
Two-fold cross validation can be computed for a wd
object using the "cv" policy option in
threshold.wd. As part of this procedure for each
threshold value that the CV optimisation algorithm selects a RSS value
must be computed (the CV optimisation algorithm seeks to minimize this
RSS value).
The RSS value computed is this. First, the even and odd indexed values are
separated. The even values are used to construct an estimate of the odd
true values using wavelet shrinkage with the given threshold. The sum
of squares between the estimate and the noisy odds is computed. An equivalent
calculation is performed by swapping the odds and evens. The two
RSS values are then averaged and the average returned. This
algorithm is described more fully in
Nason, (1996).
RELEASE
Version 3.0 Copyright Guy Nason 1994
SEE ALSO
Crsswav,
CWCV,
threshold.wd,
WaveletCV.
EXAMPLES
#
# This function is best used via the policy="cv" option in
# the threshold.wd function.
# See examples there.
#