Adaptive sequential procedures for selecting the best of several normal populations†

Abstract

There are k(≧2) competing normal populations with common known variance and unknown means . Let denote the ordered values of the {z i}. Nothing is known concerning the pairing of the {z.Θ i} and the {z.Θ [i]}. In the location invariant identification problem, the differences are given and it is desired to select the population associated with {z.Θ [k]}. Of particular interest is the slippage configuration where δ *>0 is given. We restrict attention to procedures that guarantee that the population with the largest mean is correctly selected with probability at least P * where is preassigned. Essentially, this requirement is satisfied by the stopping rule of Bechhofer, Kiefer and Sobel (Sequential Identification and Ranking Procedures, Univ. of Chicago Press 1968, Chap. 3) independently of the sampling rule and thus data dependent allocation rules can be considered. Unlike the case k=2 (see Robbins and Siegmund ( 1974) J. Am. Statist. Assoc. 69, 132-139), when k≧3,substantial savings in expected tot...