Optimal rates of convergence of empirical Bayes tests for the continuous one-parameter exponential family

• 成果类型: Article
• 署名作者: Karunamuni, RJ
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1996
• 页码: 212-231
• 关键词: geometrizing rates

摘要

The empirical Bayes linear loss two-action problem in the continuous one-parameter exponential family is studied, Previous results on this problem construct empirical Bayes tests via kernel density estimates, They also obtain upper bounds for the unconditional regret at some prior distribution. In this paper, we discuss the general question of how difficult the above empirical Bayes problem is, and why empirical Bayes rules based on kernel density estimates are useful. Asymptotic minimax-type lower bounds are obtained for the unconditional regret, and empirical Bayes rules based on kernel density estimates are shown to possess a certain optimal asymptotic minimax property.