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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
Published by: Institute of Mathematical Statistics
Stable URL: http://www.jstor.org/stable/2958949
Page Count: 16
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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.
The Annals of Statistics © 1975 Institute of Mathematical Statistics