power.sum {waveband}

Sums of wavelets raised to integer powers

Description

Computes a sum expressed in terms of mother wavelets raised to the power two, three, or four. Either the exact solution or a faster approximation can be computed.

Usage

power.sum(alphas.wd, pow = 2, verbose = TRUE, type = "approx", plotfn = FALSE)

Arguments

alphas.wd

A wd.object, the D component of which contains the coefficients of the powers of wavelets. The entry which would normalLy be the coefficient of the wavelet at scale j and location k is the coefficient of the same wavelet raised to the power pow.

If pow=2, then the overall scaling function coefficient is included in the sum, otherwise the C component is ignored completely.

The filter.number and /link{family} components of alphas.wd are used to determine which wavelet is used.

pow

The power to which the wavelets are raised; it can take values 2, 3, or 4.

verbose

If verbose=TRUE, progress reports are printed while the sum is being evaluated.

type

If type="approx", the approximation is computed, if type="exact", the exact solution is computed, and if type="both" both the exact and approximate solutions are found.

plotfn

If plotfn=TRUE, the solution(s) found are plotted.

Details

For the approximate method, the powers of mother wavelets are represented by scaling functions (father wavelets) at a finer level. This is discussed in Barber, Nason, & Silverman (2001).

Sums of powers of wavelets are used in the computation of posterior credible intervals for wavelet regression estimators; see the documentation for the function wave.band for more details.

Value

A vector containing the solution (either exact or approximate), or a list containing both solutions, depending on the value of "type".

SIDE EFFECTS

If plotfn=TRUE, the solution(s) found are plotted.

References

Barber, S., Nason, G.P. and Silverman, B.W. (2002) Posterior probability intervals for wavelet thresholding. Journal of the Royal Statistical Society, Series B, 64, 189-206.

See Also

wave.band