On the Stochastic Minimization of Sample Size by the Bechhofer-Kulkarni Bernoulli Sequential Selection Procedure

Bechhofer and Kulkarni (1982) proposed procedures for selecting that one of k Bernoulli populations with the largest single-trial success probability. They showed that their procedure for k = 2 minimizes the expected total sample size amongst a class of procedures, all of which attain the same probability of correct selection. Kulkarni and Jennison (1986) generalized this result to the case k'Z 3. In this article we prove the stronger result that the Bechhofer-Kulkami procedure for each k = 2 stochastically minimizes the distribution of sample size amongst procedures in the same class. That is, the distribution of sample size for the Bechhofer-Kulkarni procedure is the same as or stochastically smaller than that for any other procedure in the class.