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A Restricted Subset Selection Approach to Ranking and Selection Problems

Thomas J. Santner
The Annals of Statistics
Vol. 3, No. 2 (Mar., 1975), pp. 334-349
Stable URL: http://www.jstor.org/stable/2958949
Page Count: 16
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
A Restricted Subset Selection Approach to Ranking and Selection Problems
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Abstract

Let π1,⋯, πk be k populations with πi characterized by a scalar λi ∈ Λ, a specified interval on the real line. The object of the problem is to make some inference about π(k), the population with largest λi. 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 λi'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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