Calculates empirical scaling function coefficients of the probability density function from sample of data from that density, usually at some "high" resoloution.
denproj(x, tau=1, J, filter.number=10, family="DaubLeAsymm", covar=FALSE, nT=20)A list with components:
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.
Matrix containing the covariances, if requested.
The maximum and minimum values of k for which the empirical scaling function coefficients cJk are non-zero.
The primary resolution tau * 2J.
A list containing the filter.number and family specified inthe function call.
The length of the data vector x.
A list containing the values of p, tau and J.
Vector containing the data. This can be of any length.
The resolution level at which the empirical scaling function coefficients are to be calculated.
This parameter allows non-dyadic resolutions to be used,
since the resolution is specified as tau * 2J.
The filter number of the wavelet basis to be used.
The family of wavelets to use, can be "DaubExPhase" or "DaubLeAsymm".
Logical variable. If TRUE then covariances of the empirical scaling function coefficients are also calculated.
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.
David Herrick
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.
Chires5, Chires6, denwd,
denwr
# 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")
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