The Annals of Mathematical Statistics

An Empirical Bayes Approach to the Testing of Certain Parametric Hypotheses

Ester Samuel

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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.

Article information

Source
Ann. Math. Statist., Volume 34, Number 4 (1963), 1370-1385.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177703870

Digital Object Identifier
doi:10.1214/aoms/1177703870

Mathematical Reviews number (MathSciNet)
MR178554

Zentralblatt MATH identifier
0202.49304

JSTOR
links.jstor.org

Citation

Samuel, Ester. An Empirical Bayes Approach to the Testing of Certain Parametric Hypotheses. Ann. Math. Statist. 34 (1963), no. 4, 1370--1385. doi:10.1214/aoms/1177703870. https://projecteuclid.org/euclid.aoms/1177703870


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