On an empiricial Bayes test for a normal mean

• 成果类型: Article
• 署名作者: Liang, TC
• 署名单位: Wayne State University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1016218234
• 发表日期: 2000
• 页码: 648-655
• 关键词: optimal rates; CONVERGENCE

摘要

We exhibit an empirical Bayes test delta(n)(*) for the normal mean testing problem using a linear error loss. Under the condition that the critical point of a Bayes test is within some known compact interval, delta(n)(*) is shown to be asymptotically optimal and its associated regret Bayes risk converges to zero at a rate O(n(-1)(ln n)(1.5)), where n is the number of past experiences available when the current component decision problem is considered. Under the same condition this rate is faster than the optimal rate of convergence claimed by Karunamuni.