MINIMAX INVARIANT REGRET SOLUTION TO THE N-SAMPLE SLIPPAGE PROBLEM

A minimax regret test is proposed for deciding whether one of N populations has slipped to the right of the rest, under the null hypothesis that all populations are identical. The problem is formulated as a multiple decision problem under uncertainty relative to a priori distribution of hypotheses and incomplete knowledge of probability distributions of observations. For the problem with nuisance parameters we use the combination of a minimax regret approach relative to the prior distribution and an invariance principle for nuisance parameters. The resulting minimax–invariant tests can be successfully applied to a variety of particular practical problems such as detection, identification, classification, and pattern recognition. The general results are illustrated by particular examples.