CWavDE

Wavelet Density estimation

DESCRIPTION

USAGE

CWavDE(x, Jmax, threshold = 0, nout = 100, primary.resolution = 1, 
    filter.number = 10, family = "DaubLeAsymm", verbose = 0, 
    SF = NULL, WV = NULL) 

REQUIRED ARGUMENTS

x

A vector (of any length) containing data whose density you wish to estimate.

Jmax

The number of levels to use in the wavelet transform (user must select).

OPTIONAL ARGUMENTS

threshold

If set then the derived wavelet coefficient will be subject to hard thresholding with the threshold value supplied (nb this value is NOT chosen automatically and needs to be chosen by the user for proper use).

nout

The number of ordinates for the resultant density estimate (needs to be chosen by the user for best performance).

primary.resolution

The primary resolution for the scaling functions that the data, x, gets projected onto (needs to be chosen by the user for best performance).

filter.number

Specifies the family member of the wavelet family (see filter.select for more details). Only used if the SF argument is not specified. (Needs to be chosen by the user for best performance).

family

specifies the family of wavelets that you want to use (see filter.select for more details). (Needs to be chosen by the user for best performance).

verbose

Controls the printing of "informative" messages. There aren't many.

SF

A list with two components x and y. These are the (x,y) values of the scaling function to use (if this argument is not specified then the function uses the support function to generate appropriate values using filter.number and family arguments above).

WV

A list with two components x and y. These are the (x,y) values of the mother wavelet to use (if this argument is not specified then the function uses the support function to generate appropriate values using filter.number and family arguments above).

VALUE

x

X coordinate of density estimate (of length nout)

y

y coordinate of density estimate (of length nout).

sfix

The range of k translation values for the scaling functions used at the finest level.

wvixmin

The minimum of the k translation values for the wavelets at each of the Jmax scale levels.

wvixmax

The maximum of the k translation values for the wavelets at each of the Jmax scale levels.

SIDE EFFECTS

DETAILS

This code follows the procedure for computing wavelet density estimates espoused by Hall and Patil, 1995.

First, scaling function coefficients at a given primary resolution are computed by projection of the X_i values onto the father wavelets, \phi_i for all coefficients of father wavelets whose support covers X_i.

The resulting father wavelet coefficients are then subjected to a Jmax level wavelet transform. Thresholding is applied and then the estimate is constructed from the thresholded wavelet coefficients.

This piece of code is not really designed to do production density estimation but to be an exploratory tool for evaluating procedures that automatically compute parameter estimates (threshold, primary res, Jmax, etc).

RELEASE

SEE ALSO

EXAMPLES

#
# Generate some example data. A bimodal hump!
#
x <- c( rnorm(100, -2, 1), rnorm(100, 2, 1))
#
# Subject this to a wavelet density estimate.
#
tmp <- CWavDE(x, Jmax=10)
#
# Note this is not a "serious" estimate since the values of primary.resolution,
# threshold, filter.number and family would have to be chosen properly (and
#  Jmax).
#
#
# Plot the estimate
#
plot( tmp$x, tmp$y, type="l")

#
# Well, sort of bivariate! Let's make it a bit smoother.
#
# The following parameters were chosen by trial and error
#
tmp2 <-CWavDE(x, 10, filter.number=6, nout=200, primary=1, threshold=0.07)
#
# Plot the new estimate
# 
plot( tmp2$x, tmp2$y, type="l")