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May, 1978 An Adaptive Solution to Ranking and Selection Problems
Y. L. Tong
Ann. Statist. 6(3): 658-672 (May, 1978). DOI: 10.1214/aos/1176344210


An adaptive approach is considered as an alternative to the classical indifference-zone formulation of the problems of ranking and selection. With a fixed $\gamma^\ast$, the proposed procedure calls for the termination of sampling when the estimated probability of correct selection exceeds $\gamma^\ast$ for the first time. Asymptotic properties of this procedure are proved as $\gamma^\ast \rightarrow 1$, and Monte Carlo results show that the procedure is well behaved even for moderate $\gamma^\ast$. Since the stopping variables depend on the estimators of the ordered parameters, distributions of the estimators as functions of the parameters are carefully studied via majorization.


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Y. L. Tong. "An Adaptive Solution to Ranking and Selection Problems." Ann. Statist. 6 (3) 658 - 672, May, 1978.


Published: May, 1978
First available in Project Euclid: 12 April 2007

zbMATH: 0384.62025
MathSciNet: MR471150
Digital Object Identifier: 10.1214/aos/1176344210

Primary: 62F07
Secondary: 62L12

Keywords: Adaptive methods , majorization and spacings , Ranking and selection , sequential estimation , Sequential multiple decision rules

Rights: Copyright © 1978 Institute of Mathematical Statistics


Vol.6 • No. 3 • May, 1978
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