ADMISSIBLE BAYES EQUIVARIANT ESTIMATION OF LOCATION VECTORS FOR SPHERICALLY SYMMETRIC DISTRIBUTIONS WITH UNKNOWN SCALE

• 成果类型: Article
• 署名作者: Maruyama, Yuzo; Strawderman, William E.
• 署名单位: University of Tokyo; Rutgers University System; Rutgers University New Brunswick
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/19-AOS1837
• 发表日期: 2020
• 页码: 1052-1071
• 关键词: minimax estimators; BOUNDARY; PROOF

摘要

This paper investigates estimation of the mean vector under invariant quadratic loss for a spherically symmetric location family with a residual vector with density of the form f (x, u) = eta((p+ n)/2) f (eta{parallel to x - theta parallel to(2) + parallel to u parallel to(2)}), where. is unknown. We show that the natural estimator x is admissible for p = 1, 2. Also, for p >= 3, we find classes of generalized Bayes estimators that are admissible within the class of equivariant estimators of the form {1 - xi(x/parallel to u parallel to)}x. In the Gaussian case, a variant of the James-Stein estimator, [1-{(p - 2)/(n+ 2)}/{parallel to x parallel to(2)/parallel to u parallel to(2) +(p - 2)/(n+ 2) + 1}]x, which dominates the natural estimator x, is also admissible within this class. We also study the related regression model.