A Theory of some Multiple Decision Problems, I

Abstract

A class of multiple decision procedures is described and its members are shown to possess uniformly minimum risk among all procedures that are unbiased with respect to a certain loss function. This provides a justification for a number of procedures considered by Tukey, Duncan, and others, for certain classes of point estimates, and for some nonparametric decision procedures based on sample cumulative distribution functions and related to tests of the Kolmogoroff-Smirnoff type.