IS PITMAN CLOSENESS A REASONABLE CRITERION

• 成果类型: Article
• 署名作者: ROBERT, CP; HWANG, JTG; STRAWDERMAN, WE
• 署名单位: Cornell University; Rutgers University System; Rutgers University New Brunswick
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.2307/2290692
• 发表日期: 1993
• 页码: 57-63
• 关键词: multivariate normal-distribution; stochastic domination; exponential-families; universal domination; estimators; parameters

摘要

The criterion of Pitman closeness has been proposed as an alternative comparison criterion to quadratic losses and, more generally, to decision theory. However, it may lead to quite paradoxical phenomena, the most dramatic being a possible nontransitivity. The criterion takes into consideration the joint distribution of the compared estimators, but this consideration may be misleading in the selection of the ''best'' estimator. We show through examples that this criterion is not consistent with a decision theoretic analysis and that it should be used very cautiously, if ever.