sqcoefvec {hwwntest} | R Documentation |
Compute coefficients required for approximaing the wavelet transform using the square of wavelets.
Description
Essentially, part of a method for computing a wavelet-like transform using the squares of wavelets rather than the wavelets themselves.
Usage
sqcoefvec(m0, filter.number = 10, family = "DaubLeAsymm",
resolution = 4096, stop.on.error = FALSE, plot.it = FALSE)
Arguments
m0 |
The number of scales finer than the square wavelet being approximated. Usually, 2 or 3 is enough. |
filter.number |
Number of vanishing moments of underlying wavelet. |
family |
Family of underlying wavelet |
resolution |
Function values of the wavelet itself are generated by a high-resolution approximation. This argument specifies exactly how many values. |
stop.on.error |
This argument is supplied to the |
plot.it |
Plots showing the approximation are plotted. |
Details
The idea is that the square of a wavelet (the square wavelet)
is approximated by wavelets at a finer scale. The argument m0
controls how many levels below the original scale are used.
Essentially, this function computes a representation of the
original square wavelet in terms of finer scale wavelets. Hence,
when a decomposition of another function with respect to the square
wavelets is required, one can compute the representation with
respect to a regular wavelet decomposition and then apply the
wavelet to square wavelet transform to turn it into a square wavelet
representation.
This idea originally used for performing ‘powers of wavelets’ transforms in Herrick (2000) and Barber, Nason and Silverman (2002) and for the mod-wavelets is described in Fryzlewicz, Nason and von Sachs (2008).
Value
A list with the following components:
ll |
Vector containing integers between the lower and upper limit of the wavelets required at the finer scale. |
ecoef |
The appropriate coefficients that approximate the mod wavelet at the finer scale. |
m0 |
The number of scales finer below the scale that the function is at |
filter.number |
The wavelet filter number used |
family |
The wavelet family used |
ecode |
An error code, if zero then ok, otherwise returns 1 |
ians |
The actual return values from the internal call to the
|
Author(s)
Guy Nason
References
Barber, S., Nason, G.P. and Silverman, B.W. (2002) Posterior probability intervals for wavelet thresholding. J. R. Statist. Soc. B, 64, 189-206.
Fryzlewicz, P., Nason, G.P. and von Sachs, R. (2008) A wavelet-Fisz approach to spectrum estimation. J. Time Ser. Anal., 29, 868-880.
Herrick, D.R.M. (2000) Wavelet Methods for Curve Estimation, PhD thesis, University of Bristol, U.K.
Nason, G.P. and Savchev, D. (2014) White noise testing using wavelets. Stat, 3, 351-362. doi:10.1002/sta4.69
See Also
Examples
#
# This function is not really designed to be used by the casual user
#
tmp <- sqcoefvec(m0=2, filter.number=4)