Empirical Bayes block shrinkage of wavelet coefficients via the noncentral χ2 distribution

• 成果类型: Article
• 署名作者: Wang, Xue; Wood, Andrew T. A.
• 署名单位: University of Bristol; University of Nottingham
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/93.3.705
• 发表日期: 2006
• 页码: 705722
• 关键词: threshold; smoothness; RESOLUTION; selection

摘要

Empirical Bayes approaches to the shrinkage of empirical wavelet coefficients have generated considerable interest in recent years. Much of the work to date has focussed on shrinkage of individual wavelet coefficients in isolation. In this paper we propose an empirical Bayes approach to simultaneous shrinkage of wavelet coefficients in a block, based on the block sum of squares. Our approach exploits a useful identity satisfied by the noncentral chi(2) density and provides some tractable Bayesian block shrinkage procedures. Our numerical results indicate that the new procedures perform very well.