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Optimal Properties of the Bechhofer-Kulkarni Bernoulli Selection Procedure

机译：Bechhofer-Kulkarni Bernoulli选择过程的最优性质

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In a recent article Bechhofer and Kulkarni proposed a class of closed adaptive sequential procedures for selecting that one of k > or = 2 Bernoulli populations with the largest single-trial success probability. These sequential procedures which take no more than n observations from any one of the k populations achieve the same probability of a correct selection as does a single-stage procedure which takes exactly n observations from every one of the k populations. In addition, they often require substantially less than a total of kn observations to terminate sampling. Amongst other problems, Bechhofer and Kulkarni considered the problem of devising a procedure within the class which minimizes the expected total number of observations to terminate sampling. For their proposed procedure they cited several optimality properties for the case k = 2 and conjectured additional optimality properties for the case k > or = 3. In this article we used a new method of proof to establish stronger results than those cited by Bechhofer and Kulkarni for the case k = 2, and prove stronger results than those conjectured for k > or = 3. We also describe a new procedure for k > or = 3 and prove that it minimizes the expected total number of obervations to terminate sampling when all of the success probabilities are small.

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