sqndwd {hwwntest}

Compute the non-decimated squared wavelet transform.

Description

A transform of the data with respect to an expansion comprised of squared wavelets.

Usage

sqndwd(x, ec)

Arguments

x

The sequence that you want transformed, of dyadic length.

ec

A structure containing the necessary information to transform the wavelet transform of the sequence to the squared wavelet transform. This is provided by the function sqcoefvec.

Details

This function first computes the wavelet transform of the x data. Then, level by level it is retransformed into the coefficients of the squared-wavelet transform using the ec structure. Fine levels, that cannot be computed using the approximate method are computed directly by the brute-force method in sqndwdecomp. Method used is described in Fryzlewicz, Nason and von Sachs (2008), and is analogous to the ‘powers of wavelets’ transform described in Herrick (2000) and Barber, Nason and Silverman (2002).

Value

An object of class wd containing the non-decimated squared wavelet transform.

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

sqwd

Examples

#
# Random data
#
x <- rnorm(16)
#
# Compute the projection of x onto the squared wavelets... 
#
ans <- sqndwd(x, ec=sqcoefvec(m0=2, filter.number=4))