WaveThresh
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dencvwd
Calculate variances of wavlet coefficients of a p.d.f.
DESCRIPTION
Calculates the variances of the empirical wavelet coefficients by performing
a 2D wavelet decomposition on the covariance matrix of the empirical scaling
function coefficients of the probability density function.
USAGE
dencvwd(hrproj, filter.number=hrproj$filter$filter.number, family=hrproj$filter$family, type="wavelet", bc="zero", firstk=hrproj$klim, RetFather=T, verbose=F)
REQUIRED ARGUMENTS
- hrproj
- Output from denproj with
covar=T.
OPTIONAL ARGUMENTS
- filter.number
- The filter number of the wavelet basis to be used. This argument should
not be altered.
- family
- The family of wavelets to use, can be "DaubExPhase" or "DaubLeAsymm".
This argument should not be altered.
- type
- The type of decomposition to be performed. This argument should not be
altered.
- bc
- The type of boundary conditions to be used. For density estimation this
should always be zero.
- firstk
- The bounds on the translation index of the empirical scaling function
coefficients.
- RetFather
- Ignore this.
- verbose
- If
TRUE the function will be chatty. Note that comments are
only availble for part of the algorithm, so might not be very enlightening.
VALUE
An object of class wd.
DETAILS
This function is basically
imwd
adapted to handle zero boundary conditions, except that only the variances
are returned, i.e. the diagonals of the covariance matrices produced. Note
that this code is not very efficient. The full covariance matrices of all
levels of coefficients are calculated, and then the diagonals are extracted.
SEE ALSO
`denproj',
`imwd'
# Simulate data from the claw density, find the
# empirical scaling function coefficients and covariances and then decompose
# both to give wavelet coefficients and their variances.
data <- rclaw(100)
datahr <- denproj(data, J=8, filter.number=2,family="DaubExPhase", covar=T)
data.wd <- denwd(datahr)
plotdenwd(data.wd, top.level=(datahr$res$J-1))
datavar <- dencvwd(datahr)
plotdenwd(datavar, top.level=(datahr$res$J-1))
AUTHOR
David Herrick