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March, 1975 A Restricted Subset Selection Approach to Ranking and Selection Problems
Thomas J. Santner
Ann. Statist. 3(2): 334-349 (March, 1975). DOI: 10.1214/aos/1176343060

Abstract

Let $\pi_1,\cdots, \pi_k$ be $k$ populations with $\pi_i$ characterized by a scalar $\lambda_i \in \Lambda$, a specified interval on the real line. The object of the problem is to make some inference about $\pi_{(k)}$, the population with largest $\lambda_i$. The present work studies rules which select a random number of populations between one and $m$ where the upper bound, $m$, is imposed by inherent setup restrictions of the subset selection and indifference zone approaches. A selection procedure is defined in terms of a set of consistent sequences of estimators for the $\lambda_i$'s. It is proved the infimum of the probability of a correct selection occurs at a point in the preference zone for which the parameters are as close together as possible. Conditions are given which allow evaluation of this last infimum. The number of non-best populations selected, the total number of populations selected, and their expectations are studied both asymptotically and for fixed $n$. Other desirable properties of the rule are also studied.

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Thomas J. Santner. "A Restricted Subset Selection Approach to Ranking and Selection Problems." Ann. Statist. 3 (2) 334 - 349, March, 1975. https://doi.org/10.1214/aos/1176343060

Information

Published: March, 1975
First available in Project Euclid: 12 April 2007

zbMATH: 0302.62011
MathSciNet: MR370884
Digital Object Identifier: 10.1214/aos/1176343060

Subjects:
Primary: 62F07
Secondary: 62G30

Keywords: multiple decision , Ranking and selection , restricted subset size

Rights: Copyright © 1975 Institute of Mathematical Statistics

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Vol.3 • No. 2 • March, 1975
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