| denproj {wavethresh} | R Documentation |
Calculate empirical scaling function coefficients of a p.d.f.
Description
Calculates empirical scaling function coefficients of the probability density function from sample of data from that density, usually at some "high" resoloution.
Usage
denproj(x, tau=1, J, filter.number=10, family="DaubLeAsymm", covar=FALSE, nT=20)
Arguments
x |
Vector containing the data. This can be of any length. |
J |
The resolution level at which the empirical scaling function coefficients are to be calculated. |
tau |
This parameter allows non-dyadic resolutions to be used,
since the resolution is specified as |
filter.number |
The filter number of the wavelet basis to be used. |
family |
The family of wavelets to use, can be "DaubExPhase" or "DaubLeAsymm". |
covar |
Logical variable. If TRUE then covariances of the empirical scaling function coefficients are also calculated. |
nT |
The number of iterations to be performed in the Daubechies-Lagarias algorithm, which is used to evaluate the scaling functions of the specified wavelet basis at the data points. |
Details
This projection of data onto a high resolution wavelet space is described in
detail in Chapter 3 of Herrick (2000).
The maximum and minimum values of k for which the empirical scaling
function coefficient is non-zero are determined and
the coefficients calculated for all k between these limits as
sum(phiJk(xi))/n.
The scaling functions are evaluated at the data points efficiently,
using the Daubechies-Lagarias algorithm (Daubechies & Lagarias (1992)).
Coded kindly by Brani Vidakovic.
Herrick, D.R.M. (2000) Wavelet Methods for Curve and Surface Estimation. PhD Thesis, University of Bristol.
Daubechies, I. & Lagarias, J.C. (1992). Two-Scale Difference Equations II. Local Regularity, Infinite Products of Matrices and Fractals. SIAM Journal on Mathematical Analysis, 24(4), 1031–1079.
Value
A list with components:
coef |
A vector containing the empirical scaling function coefficients. This starts with the first non-zero coefficient, ends with the last non-zero coefficient and contains all coefficients, including zeros, in between. |
covar |
Matrix containing the covariances, if requested. |
klim |
The maximum and minimum values of k for which the empirical scaling function coefficients cJk are non-zero. |
p |
The primary resolution |
filter |
A list containing the filter.number and family specified inthe function call. |
n |
The length of the data vector x. |
res |
A list containing the values of |
Author(s)
David Herrick
See Also
Chires5, Chires6, denwd,
denwr
Examples
# Simulate data from the claw density and find the
# empirical scaling function coefficients
data <- rclaw(100)
datahr <- denproj(data, J=8, filter.number=4,family="DaubLeAsymm")