Minimax Subset Selection for Loss Measured by Subset Size

Abstract

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 noncentrality parameters, such as $\chi^2$ and $F$, previously proposed rules are found to be not minimax.