Statistics Papers

Document Type

Journal Article

Date of this Version

2000

Publication Source

Journal of the Royal Statistical Society. Series B

Volume

62

Issue

4

Start Page

681

Last Page

698

DOI

10.1111/1467-9868.00257

Abstract

Wavelet shrinkage estimation is an increasingly popular method for signal denoising and compression. Although Bayes estimators can provide excellent mean-squared error (MSE) properties, the selection of an effective prior is a difficult task. To address this problem, we propose empirical Bayes (EB) prior selection methods for various error distributions including the normal and the heavier-tailed Student t-distributions. Under such EB prior distributions, we obtain threshold shrinkage estimators based on model selection, and multiple-shrinkage estimators based on model averaging. These EB estimators are seen to be computationally competitive with standard classical thresholding methods, and to be robust to outliers in both the data and wavelet domains. Simulated and real examples are used to illustrate the flexibility and improved MSE performance of these methods in a wide variety of settings.

Copyright/Permission Statement

This is the peer reviewed version of the following article: Clyde, M. and George, E. I. (2000), Flexible empirical Bayes estimation for wavelets. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 62: 681–698., which has been published in final form at doi: 10.1111/1467-9868.00257. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving http://olabout.wiley.com/WileyCDA/Section/id-820227.html#terms.

Keywords

Bayesian model averaging, EM algorithm, hierarchical models, model selection, multiple shrinkage, orthogonal regression, outliers, robustness, thresholding

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Date Posted: 27 November 2017

This document has been peer reviewed.