Asymptotically optimal and admissible decision rules in compound compact Gaussian shift experiments

• 成果类型: Article
• 署名作者: Majumdar, S
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1996
• 页码: 196-211
• 关键词: families; BAYES

摘要

Asymptotically optimal and admissible compound decision rules are obtained in a Hilbert-parameterized Gaussian shift experiment. The component parameter set is restricted to compact. For the squared error loss, every compound Bayes estimator is admissible and every compound estimator Bayes versus full support hyperprior mixture of lid priors on the compound parameter is asymptotically optimal. For the latter class of rules induced by full support hyperpriors, asymptotic optimality and admissibility extend to equi- (in decisions) uniformly continuous and bounded risk functions. Normality of certain mixtures of the standard Gaussian process and qualitative robustness of the component Bayes estimator (results of independent interest used in the paper) are derived.