A NOTE ON ADMISSIBILITY WHEN PRECISION IS UNBOUNDED

• 成果类型: Article
• 署名作者: ANDERSON, C; PAL, N
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176324537
• 发表日期: 1995
• 页码: 593-597
• 关键词: bayes minimax estimators; MULTIVARIATE

摘要

The estimation of a common mean vector theta given two independent normal observations X similar to N-p(theta, rho(x)(2)I) and Y similar to N-p(theta, rho(y)(2)I) is reconsidered. It being known that the estimator eta X + (1 - eta)Y is inadmissible when eta is an element of (0,1), we show that when eta is 0 or 1, then the opposite is true, that is, the estimator is admissible. The general situation is that an estimator X* can be improved by shrinkage when there exists a statistic B which, in a certain sense, estimates a lower bound on the risk of X*. On the other hand, an estimator is admissible under very general conditions if there is no reasonable way to detect that its risk is small.