Empirical Bayes approach to block wavelet function estimation

Abramovich, Felix and Besbeas, Panagiotis and Sapatinas, Theofanis (2002) Empirical Bayes approach to block wavelet function estimation. Computational Statistics and Data Analysis, 39 (4). pp. 435-451. ISSN 0167-9473 . (The full text of this publication is not available from this repository)

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Abstract

Wavelet methods have demonstrated considerable success in function estimation through term-by-term thresholding of the empirical wavelet coefficients, However, it has been shown that grouping the empirical wavelet coefficients into blocks and making simultaneous threshold decisions about all the coefficients in each block has a number of advantages over term-by-term wavelet thresholding, including asymptotic optimality and better mean squared error performance in finite sample situations. An empirical Bayes approach to incorporating information on neighbouring empirical wavelet coefficients into function estimation that results in block wavelet shrinkage and block wavelet thresholding estimators is considered. Simulated examples are used to illustrate the performance of the resulting estimators, and to compare these estimators with several existing non-Bayesian block wavelet thresholding estimators. It is observed that the proposed empirical Bayes block wavelet shrinkage and block wavelet thresholding estimators outperform the non-Bayesian block wavelet thresholding estimators in finite sample situations. An application to a data set that was collected in an anaesthesiological study is also presented. (C) 2002 Elsevier Science B.V. All rights reserved.

Item Type: Article
Uncontrolled keywords: empirical Bayes; block thresholding; maximum likelihood estimation; non-parametric regression; wavelet transform
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Statistics
Depositing User: Judith Broom
Date Deposited: 09 Sep 2008 18:52
Last Modified: 09 May 2014 14:09
Resource URI: http://kar.kent.ac.uk/id/eprint/6764 (The current URI for this page, for reference purposes)
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