power.sum {waveband} | R Documentation

## 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.

### See Also

`wave.band`

[Package waveband version 4.0-2 Index]