On the Small-Sample Properties of the Olkin-Sobel-Tong Estimator of the Probability of Correct Selection

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Abstract
In the problem of selecting the best of k populations, Olkin, Sobel, and Tong (1976) have introduced the important idea of a posteriori analysis of the data (as opposed to the usual formulation), in which design of the experiment is the major consideration. They considered the large-sample properties of an estimator that has been discussed further by Gibbons, Olkin, and Sobel (1977), Gupta and Panchapakesan (1979), and Tong (1980). In this article we study the small-sample performance of the Olkin, Sobel, and Tong estimator, analytically for k = 2 populations and via Monte Carlo simulation for k ≥ 2 populations in the normal means, common, known variance case. This small-sample performance is found to have some serious shortcomings.

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