LOWER BOUNDS FOR THE ASYMPTOTIC BAYES RISK IN THE SCALE-MODEL (WITH AN APPLICATION TO THE 2ND-ORDER MINIMAX ESTIMATION)

• 成果类型: Article
• 署名作者: GAJEK, L; KALUSZKA, M
• 署名单位: Polish Academy of Sciences
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176325759
• 发表日期: 1994
• 页码: 1831-1839
• 关键词: parameter space

摘要

The problem of Bayes estimation of the scale parameter is considered. Lower bounds for the asymptotic Bayes risk are given as the restricted parameter space increases to the positive half-line. The results are next applied to establish the second-order minimax estimator of the scale parameter. Surprisingly, the least favorable distribution coincides with that for the corresponding location parameter problem.