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December, 1958 Most Economical Multiple-Decision Rules
Wm. Jackson Hall
Ann. Math. Statist. 29(4): 1079-1094 (December, 1958). DOI: 10.1214/aoms/1177706442


This paper is concerned with non-sequential multiple-decision procedures for which the sample size is a minimum subject to either (1) lower bounds on the probabilities of making correct decisions or (2) upper bounds on the probabilities of making incorrect decisions. Such decision procedures are obtained by constructing artificial decision problems for which the minimax strategies provide solutions to problems (1) and (2). These are shown to be "likelihood ratio" and "unlikelihood ratio" decision rules, respectively. Thus, although problems (1) and (2) are formulated in the spirit of the classical Neyman-Pearson approach to two-decision problems, minimax theory is used as a tool for their solution. Problems of both "simple" and "composite" discrimination are considered and some examples indicated. (Some multivariate examples are given in [4].) Various properties of the decision rules are derived, and relationships with works of Wald, Lindley, Rao and others are cited.


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Wm. Jackson Hall. "Most Economical Multiple-Decision Rules." Ann. Math. Statist. 29 (4) 1079 - 1094, December, 1958.


Published: December, 1958
First available in Project Euclid: 27 April 2007

zbMATH: 0099.13405
MathSciNet: MR100328
Digital Object Identifier: 10.1214/aoms/1177706442

Rights: Copyright © 1958 Institute of Mathematical Statistics

Vol.29 • No. 4 • December, 1958
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