Most Economical Multiple-Decision Rules

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 obt...

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Bibliographic Details
Published inThe Annals of mathematical statistics Vol. 29; no. 4; pp. 1079 - 1094
Main Author Hall, Wm. Jackson
Format Journal Article
LanguageEnglish
Published Institute of Mathematical Statistics 01.12.1958
The Institute of Mathematical Statistics
Subjects
A priori knowledge
Bayes theorem
Decision making
Economic theory
Integers
Mathematical functions
Minimax
Sample size
Statistics
Weighting functions
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Summary: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.
ISSN:0003-4851
2168-8990
DOI:10.1214/aoms/1177706442