Open Access
July, 1981 A Class of Schur Procedures and Minimax Theory for Subset Selection
Jan F. Bjornstad
Ann. Statist. 9(4): 777-791 (July, 1981). DOI: 10.1214/aos/1176345518

Abstract

The problem of selecting a random subset of good populations out of $k$ populations is considered. The populations $\Pi_1, \cdots, \Pi_k$ are characterized by the location parameters $\theta_1, \cdots, \theta_k$ and $\Pi_i$ is said to be a good population if $\theta_i > \max_{1 \leq j\leq k}\theta_j - \Delta$, and a bad population if $\theta_i \leq \max_{1 \leq j \leq k} \theta_j - \Delta$, where $\Delta$ is a specified positive constant. A theory for a special class of procedures, called Schur procedures, is developed, and applied to certain minimax problems. Subject to controlling the minimum expected number of good populations selected or the probability that the best population is in the selected subset, procedures are derived which minimize the expected number of bad populations selected or some similar criterion. For normal populations it is known that the classical "maximum-type" procedures has certain minimax properties. In this paper, two other procedures are shown to have several minimax properties. One is the "average-type" procedure. The other procedure has not previously been considered as a serious contender.

Citation

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Jan F. Bjornstad. "A Class of Schur Procedures and Minimax Theory for Subset Selection." Ann. Statist. 9 (4) 777 - 791, July, 1981. https://doi.org/10.1214/aos/1176345518

Information

Published: July, 1981
First available in Project Euclid: 12 April 2007

zbMATH: 0475.62016
MathSciNet: MR619281
Digital Object Identifier: 10.1214/aos/1176345518

Subjects:
Primary: 62F07
Secondary: 26A51‎ , 62C99

Keywords: location model , minimax procedures , Schur-concave functions , subset selection

Rights: Copyright © 1981 Institute of Mathematical Statistics

Vol.9 • No. 4 • July, 1981
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