Brown's paradox in the estimated confidence approach

• 成果类型: Article
• 署名作者: Wang, HY
• 署名单位: Academia Sinica - Taiwan
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1018031210
• 发表日期: 1999
• 页码: 610-626
• 关键词: conditional properties; statistical procedures

摘要

A widely held notion of classical conditional theory is that statistical inference in the presence of ancillary statistics should he independent of the distribution of those ancillary statistcs. In this paper, ancillary paradoxes which contradict this notion are presented for two scenarios involving confidence estimation. These results are related to Brown's ancillary paradox in point estimation. Moreover, the confidence coefficient, the usual constant coverage probability estimator, is shown to be inadmissible for confidence estimation in the multiple regression model with random predictor variables if the dimension of the slope parameters is greater than five. Some estimators better than the confidence coefficient are provided in this paper. These new estimators are constructed based on empirical Bayes estimators.