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power.sum

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

function(alphas.wd, pow = 2, verbose = T, type = "approx", plotfn = F)

REQUIRED 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 family components of alphas.wd are used to determine which wavelet is used.

OPTIONAL ARGUMENTS

pow: The power to which the wavelets are raised; it can take values 2, 3, or 4.
verbose: If verbose=T, 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=T, the solution(s) found are plotted.

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=T, 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.

RELEASE

3.9.7