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.
power.sum(alphas.wd, pow = 2, verbose = TRUE, type = "approx", plotfn = FALSE)A vector containing the solution (either exact or approximate), or a list containing both solutions, depending on the value of "type".
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.
The power to which the wavelets are raised; it can take values 2, 3, or 4.
If verbose=TRUE, progress reports are printed while the sum is being evaluated.
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.
If plotfn=TRUE, the solution(s) found are plotted.
If plotfn=TRUE, the solution(s) found are plotted.
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.
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.
wave.band