ON CHARLES STEIN'S CONTRIBUTIONS TO (IN)ADMISSIBILITY

• 成果类型: Article
• 署名作者: Strawderman, William E.
• 署名单位: Rutgers University System; Rutgers University New Brunswick
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/21-AOS2108
• 发表日期: 2021
• 页码: 1823-1835
• 关键词: inadmissibility; Admissibility; estimator

摘要

Charles Stein made fundamental contributions to admissibility and inadmissibility in estimation and testing. This paper surveys some of the more important ones. Particular attention will be paid to his monumentally important, and at the time, incredibly surprising discovery of the inadmissibility of the usual estimator of the mean in three and higher dimensions. His result on admissibility of Pitman's estimator of a mean in one and two dimensions, and his results on estimation of a mean matrix and a covariance matrix are also discussed. His work on testing is briefly covered.