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.
Citation
Roger L. Berger. "Minimax Subset Selection for Loss Measured by Subset Size." Ann. Statist. 7 (6) 1333 - 1338, November, 1979. https://doi.org/10.1214/aos/1176344851
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