Abstract
Abstract Let π 1 ,…, π k represent k (⩾2) independent populations. The quality of the i th population π i is characterized by a real-valued parameter θ i , usually unknown. We define the best population in terms of a measure of separation between θ i 's. A selection of a subset containing the best population is called a correct selection (CS). We restrict attention to rules for which the size of the selected subset is controlled at a given point and the infimum of the probability of correct selection over the parameter space is maximized. The main theorem deals with construction of an essentially complete class of selection rules of the above type. Some classical subset selection rules are shown to belong to this class.
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