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December, 1963 An Empirical Bayes Approach to the Testing of Certain Parametric Hypotheses
Ester Samuel
Ann. Math. Statist. 34(4): 1370-1385 (December, 1963). DOI: 10.1214/aoms/1177703870

Abstract

The empirical Bayes approach is described in Section 2. In Section 3 "optimal" empirical Bayes rules are given for the problem of testing a simple hypothesis against a simple alternative. In Section 4 a limit theorem is proved which is used in Section 5 to obtain "optimal" empirical Bayes rules for testing one and two-sided hypotheses about the parameters in the Poisson, geometric, negative binomial and binomial distributions. The same methods are used in Section 6 to obtain "optimal" empirical Bayes rules for testing hypotheses about parameters in continuous distributions of the exponential family. Examples of areas of applications are given in Section 7, and the last Section discusses uses of the above methods in the compound decision problem.

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Ester Samuel. "An Empirical Bayes Approach to the Testing of Certain Parametric Hypotheses." Ann. Math. Statist. 34 (4) 1370 - 1385, December, 1963. https://doi.org/10.1214/aoms/1177703870

Information

Published: December, 1963
First available in Project Euclid: 27 April 2007

zbMATH: 0202.49304
MathSciNet: MR178554
Digital Object Identifier: 10.1214/aoms/1177703870

Rights: Copyright © 1963 Institute of Mathematical Statistics

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Vol.34 • No. 4 • December, 1963
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