General empirical Bayes wavelet methods and exactly adaptive minimax estimation

• 成果类型: Article
• 署名作者: Zhang, CH
• 署名单位: Rutgers University System; Rutgers University New Brunswick
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053604000000995
• 发表日期: 2005
• 页码: 54-100
• 关键词: asymptotic equivalence; DENSITY-ESTIMATION; Nonparametric Regression; spatial adaptation; threshold rules; RISK; smoothness; kernel

摘要

In many statistical problems, stochastic signals can be represented as a sequence of noisy wavelet coefficients. In this paper. we develop general empirical Bayes methods for the estimation of true signal, Our estimators approximate certain oracle separable rules and achieve adaptation to ideal risks and exact minimax risks in broad collections of classes of signals, In particular, our estimators are Uniformly adaptive to the minimum risk of separable estimators and the exact minimax risks Simultaneously in Besov balls of all smoothness and shape indices, and they are uniformly superefficient in convergence rates in all compact sets it Besov spaces with a finite secondary shape parameter. Furthermore. in classes nested between Besov balls of the same smoothness index. our estimators dominate threshold and James-Stein estimators within an infinitesimal fraction of the minimax risks. More general block empirical Bayes estimators are developed. Both white noise with drift and nonparametric regression;Ire considered.