power.sum {waveband} | R Documentation |
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)
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. |
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.
A vector containing the solution (either exact or approximate), or a list containing both solutions, depending on the value of "type".
If plotfn=TRUE
, the solution(s) found are plotted.