Bayes and Minimax Sample-Admissible Multivariate Selection Procedures
针对多个多元正态分布总体，研究如何选出δ*帕累托最优子集，并基于损失函数评估极小化极大和贝叶斯选择策略。
Abstract Let P be a class of independent populations each having an underlying multivariate normal distribution with unknown mean vector. Independent vector samples of common size n are drawn from each population in P. We say that a subset G of P is δ*-Pareto-optimal (in P) if no other population in P has the property that each component of its mean vector is larger by at least δ* ≥ 0 than the corresponding component of the mean vector of any given population in G. This article treats the problem of devising and evaluating strategies for selecting the (unique) subset G of P that is δ*-Pareto-optimal. We note that the set G as defined above is unique, nonempty, always exists, and may turn out to be the whole class P. Procedures devised to select the δ*-Pareto-optimal subset of populations are evaluated by means of loss functions that penalize the practitioner for the incorrect exclusion (inclusion) of populations that belong (do not belong) to the set G of δ*-Pareto-optimal populations. Minimax and Bayes procedures in this framework are discussed.