Minimax Subset Selection for Loss Measured by Subset Size.

摘要

A subset selection problem is formulated as a multiple decision problem. Then restricting attention to rules which attain a certain minimum probability of correct selection, the minimax value is computed, under general conditions, for loss measured by subset size and number of non-best populations selected. Applying this to location and scale problems, previously proposed rules are found to be minimax. But for problems involving binomial, multinomial and multivariate non-centrality parameters, such as chi square and F, previously proposed rules are found to be not minimax. A class of rules which has been proposed for the location problem is investigated and rules in this class are found to be not minimax in some cases. (Author)