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   -> Volume 4, Issue 11

Preprint: Vannucci-Vidakovic: Wavelet density estimation (4)
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Brani Vidakovic (

PostPosted: Fri Dec 06, 2002 9:36 am    
Subject: Preprint: Vannucci-Vidakovic: Wavelet density estimation (4)
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Preprint: Vannucci-Vidakovic: Wavelet density estimation (4)

Four Manuscripts are available. or ftp.isds.du

Any comment is welcome.

1. "Nonparametric Density Estimation using Wavelets "

Marina Vannucci University of Florence Italy

This paper addresses the problem of density estimation using the
Daubechies wavelets. Wavelet density estimators have been proposed by
several authors. It has been shown that the local nature of wavelet
functions makes these estimators competitive with classical projection
estimators. Further, the problem of negative estimates can be
rectified by estimating the square root of the density. This paper
starts with a review of classical and wavelet density estimators. Then
an extension of the univariate to the multivariate case is
presented. Finally, an application to a bivariate dataset is

File: ftp.isds.du/pub/WorkingPapers/

2. "PREVENTING THE DIRAC DISASTER:Wavelet Based Density Estimation"

Marina Vannucci University of Florence Italy
Brani Vidakovic Duke University USA

This paper addresses the problem of optimal number of basis functions
in the wavelet series estimator of density. It is a well known that
projection estimators tend to overfit the density if the number of
basis functions in the orthogonal expansion is too large. In extreme
cases the estimator is close to the Dirac function concentrated at the
observations. By exploiting the idea of Good and Gaskins (1971) an
objective way of determining the number of levels in the wavelet
density estimate using the Fisher information functional as a
roughness penalty measure is proposed. The method is exemplified on
the galaxy and old faithful geyser data sets as well as on some
simulated data.

File: ftp.isds.du/pub/Users/brani/papers/
or ftp.isds.du/pub/WorkingPapers/ (264Kb)

3. On wavelet scalograms and their applications in economic time series

By Miguel A. Ari~{n}o} Universidad de Navarra
and Brani Vidakovic
Duke University

{f Abstract.} The scalogram is the discrete wavelet transformation (DWT) counterpart
to the well-known notion of periodogram in the spectral
analysis of time series. In the same manner as the periodogram
produces an ANOVA decomposition of energy of a signal to different
Fourier frequencies, the scalogram decomposes the energy to
``level components."
In this paper we show how DWT and scalograms can be used in
detecting and separating periodic components in time series.
The proposed method is exemplified with a Spanish cement
production data set.

oindent{f Key words and phrases:} Wavelets, Time series, Scalograms.

File: ftp.isds.du/pub/Users/brani/papers/ 353 Kb

4. Bayesian Inference with Wavelets: Density Estimation

{large {sc Peter M"uller} and {sc Brani Vidakovic}}

We propose a prior probability model in the wavelet coefficient
space. The proposed model approaches wavelet coefficient thresholding
by full posterior inference in a coherent probability
model. We introduce a prior probability model with mixture
priors for the wavelet coefficients $d_{jk}$. The prior includes
a positive prior probability mass for zero coefficients. This
naturally leads to non-linear a posteriori shrinkage and thresholding
on the coefficients. We discuss an efficient posterior simulation
scheme to implement inference in the proposed model.
The discussion is focused on the density estimation problem. However,
the introduced prior probability model on the wavelet coefficient
space is general.

{it Keywords:} Wavelet decomposition; Model choice;
Density estimation; Posterior simulation.

File: ftp.isds.du/pub/Users/brani/papers/ 241 Kb

Comments welcome.

Note from the editor:
Check that Brani Vidakovic's machine listens to the name DAUB4 !
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