Frequentist optimality of Bayesian wavelet shrinkage rules for Gaussian and non-Gaussian noise

• 成果类型: Article
• 署名作者: Pensky, Marianna
• 署名单位: State University System of Florida; University of Central Florida
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053606000000128
• 发表日期: 2006
• 页码: 769-807
• 关键词: selection

摘要

The present paper investigates theoretical performance of various Bayesian wavelet shrinkage rules in a nonparametric regression model with i.i.d. errors which are not necessarily normally distributed. The main purpose is comparison of various Bayesian models in terms of their frequentist asymptotic optimality in Sobolev and Besov spaces. We establish a relationship between hyperparameters, verify that the majority of Bayesian models studied so far achieve theoretical optimality, state which Bayesian models cannot achieve optimal convergence rate and explain why it happens.