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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 where denotes the risk due to possible wrong decisions when is the true parameter point. If an a priori probability distribution of is given, a decision procedure which minimizes the expected value of 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 . Under some weak conditions, for any decision procedure not in there exists a decision procedure in such that identically in . Here is the risk function associated with , and is the risk function associated with . 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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