OATAO - Open Archive Toulouse Archive Ouverte Open Access Week

Wavelet Estimators in Nonparametric Regression: A Comparative Simulation Study

Antoniadis, Anestis and Bigot, Jérémie and Sapatinas, Theofanis Wavelet Estimators in Nonparametric Regression: A Comparative Simulation Study. (2001) Journal of Statistical Software, 6 (6). 1-83. ISSN 1548-7660

[img]
Preview
(Document in English)

PDF (Author's version) - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
661kB

Official URL: http://www.jstatsoft.org/v06/i06

Abstract

Wavelet analysis has been found to be a powerful tool for the nonparametric estimation of spatially-variable objects. We discuss in detail wavelet methods in nonparametric regression, where the data are modelled as observations of a signal contaminated with additive Gaussian noise, and provide an extensive review of the vast literature of wavelet shrinkage and wavelet thresholding estimators developed to denoise such data. These estimators arise from a wide range of classical and empirical Bayes methods treating either individual or blocks of wavelet coefficients. We compare various estimators in an extensive simulation study on a variety of sample sizes, test functions, signal-to-noise ratios and wavelet filters. Because there is no single criterion that can adequately summarise the behaviour of an estimator, we use various criteria to measure performance in finite sample situations. Insight into the performance of these estimators is obtained from graphical outputs and numerical tables. In order to provide some hints of how these estimators should be used to analyse real data sets, a detailed practical step-by-step illustration of a wavelet denoising analysis on electrical consumption is provided. Matlab codes are provided so that all figures and tables in this paper can be reproduced.

Item Type:Article
Additional Information:Thanks to American Statistical Association editor. The definitive version is available at http://www.jstatsoft.org/v06/i06
HAL Id:hal-00823485
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:Other partners > Université Joseph Fourier Grenoble 1 - UJF (FRANCE)
Other partners > University of Cyprus - UCY (CYPRUS)
Laboratory name:
Statistics:download
Deposited By: Jérémie Bigot
Deposited On:16 May 2013 08:36

Repository Staff Only: item control page