threshold.mwd: Use threshold on an mwd object.

Description

Applies hard or soft thresholding to multiple wavelet decomposition object mwd.object.

Usage

# S3 method for mwd
threshold(mwd, levels = 3:(nlevelsWT(mwd) - 1), type = "hard",
    policy = "universal", boundary = FALSE, verbose = FALSE,
    return.threshold = FALSE, threshold = 0, covtol = 1e-09, 
    robust = TRUE, return.chisq = FALSE,
    bivariate = TRUE, …)

Arguments

mwd

The multiple wavelet decomposition object that you wish to threshold.

levels

a vector of integers which determines which scale levels are thresholded in the decomposition. Each integer in the vector must refer to a valid level in the mwd object supplied. This is usually any integer from 0 to nlevelsWT(wd)-1 inclusive. Only the levels in this vector contribute to the computation of the threshold and its application.

type

determines the type of thresholding this can be "hard" or "soft".

policy

selects the technique by which the threshold value is selected. Each policy corresponds to a method in the literature. At present the different policies are "universal", "manual", "single". The policies are described in detail below.

boundary

If this argument is TRUE then the boundary bookeeping values are included for thresholding, otherwise they are not.

verbose

if TRUE then the function prints out informative messages as it progresses.

return.threshold

If this option is TRUE then the actual value of the threshold is returned. If this option is FALSE then a thresholded version of the input is returned.

threshold

This argument conveys the user supplied threshold. If the policy="manual" then value is the actual threshold value. Any other policy means that the threshold value is ignored.

covtol

The tolerance for what constitutes a singular variance matrix. If smallest eigenvalue of the estimated variance matrix is less than covtol then it is assumed to be singular and no thresholding is done at that level. Note: do not confuse covtol with cvtol an argument in threshold.wd.

robust

If TRUE the variance matrix at each level is estimated using a robust method (mad) otherwise it is estimated using var().

return.chisq

If TRUE the vector of values to be thresholded is returned. These values are a quadratic form of each coefficient vector, and under normal assumptions the noise component will have a chi-squared distribution (see Downie and Silverman 1996).

bivariate

this line is in construction

…

any other arguments

Value

An object of class mwd. This object contains the thresholded wavelet coefficients. Note that if the return.threshold option is set to TRUE then the threshold values will be returned, or if return.chisq the vector of values to be thresholded will be returned, rather than the thresholded object.

RELEASE

Details

Thresholding modifies the coefficients within a mwd.object. The modification can be performed either with a "hard" or "soft" thresholding selected by the type argument.

Unless policy="single", the following method is applied. The columns of mwd$D are taken as coefficient vectors $D_{j, k}$ . From these $χ_{j, k}^{2} = D_{j, k} \cdot V_{j}^{- 1}$ . $D_{j, k}$ is computed, where $V_{j}^{- 1}$ is the inverse of the estimated variance of the coefficient vectors in that level (j). $χ_{j, k}^{2}$ is a positive scalar which is to be thresholded in a similar manner to univariate hard or soft thresholding. To obtain the new values of $D_{j, k}$ shrink the vector by the same proportion as was the corresponding $χ_{j, k}^{2}$ term. i

Examples

Run this code

# NOT RUN {
#
# Generate some test data
#
test.data <- example.1()$y 
# }
# NOT RUN {
ts.plot(test.data)
# }
# NOT RUN {
#
# Generate some noisy data
#
ynoise <- test.data + rnorm(512, sd=0.1)
##
# Plot it
#
# }
# NOT RUN {
ts.plot(ynoise)
# }
# NOT RUN {
#
# Now take the discrete multiple wavelet transform
# N.b. I have no idea if the default wavelets here are appropriate for
# this particular examples. 
#
ynmwd <- mwd(ynoise)
# }
# NOT RUN {
plot(ynwd)
# }
# NOT RUN {
# [1] 2.020681 2.020681 2.020681 2.020681 2.020681 2.020681 2.020681
#
# Now do thresholding. We'll use the default arguments.
#
ynmwdT <- threshold(ynmwd)
#
# And let's plot it
#
# }
# NOT RUN {
plot(ynmwdT)
# }
# NOT RUN {
#
# Let us now see what the actual estimate looks like
#
ymwr <- wr(ynmwdT)
#
# Here's the estimate... 
#
# }
# NOT RUN {
ts.plot(ywr1)
# }

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