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December, 1947 An Essentially Complete Class of Admissible Decision Functions
Abraham Wald
Ann. Math. Statist. 18(4): 549-555 (December, 1947). DOI: 10.1214/aoms/1177730345

Abstract

With any statistical decision procedure (function) there will be associated a risk function r(θ) where r(θ) denotes the risk due to possible wrong decisions when θ is the true parameter point. If an a priori probability distribution of θ is given, a decision procedure which minimizes the expected value of r(θ) is called the Bayes solution of the problem. The main result in this note may be stated as follows: Consider the class C of decision procedures consisting of all Bayes solutions corresponding to all possible a priori distributions of θ. Under some weak conditions, for any decision procedure T not in C there exists a decision procedure T in C such that r(θ)r(θ) identically in θ. Here r(θ) is the risk function associated with T, and r(θ) is the risk function associated with T. Applications of this result to the problem of testing a hypothesis are made.

Citation

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Abraham Wald. "An Essentially Complete Class of Admissible Decision Functions." Ann. Math. Statist. 18 (4) 549 - 555, December, 1947. https://doi.org/10.1214/aoms/1177730345

Information

Published: December, 1947
First available in Project Euclid: 28 April 2007

zbMATH: 0029.30604
MathSciNet: MR23499
Digital Object Identifier: 10.1214/aoms/1177730345

Rights: Copyright © 1947 Institute of Mathematical Statistics

Vol.18 • No. 4 • December, 1947
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