The Annals of Statistics

Empirical Bayes Estimation of a Binomial Parameter Via Mixtures of Dirichlet Processes

Donald A. Berry and Ronald Christensen

Full-text: Open access

Abstract

The theory of Dirichlet processes is applied to the empirical Bayes estimation problem in the binomial case. The approach is Bayesian rather than being empirical Bayesian. When the prior is a Dirichlet process the posterior is a mixture of Dirichlet processes. Explicit estimators are given for the case of 2 and 3 parameters and compared with other empirical Bayes estimators by way of examples. Since the number of calculations become enormous when the number of parameters gets larger than 2 or 3 we propose two approximations for estimators of a particular parameter and compare their performance using examples.

Article information

Source
Ann. Statist., Volume 7, Number 3 (1979), 558-568.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176344677

Digital Object Identifier
doi:10.1214/aos/1176344677

Mathematical Reviews number (MathSciNet)
MR527491

Zentralblatt MATH identifier
0407.62018

JSTOR
links.jstor.org

Subjects
Primary: 62C10: Bayesian problems; characterization of Bayes procedures
Secondary: 62F15: Bayesian inference 62F10: Point estimation

Keywords
Empirical Bayes estimation Dirichlet processes mixtures of Dirichlet processes approximating mixtures of Dirichlet processes binomial parameter estimation

Citation

Berry, Donald A.; Christensen, Ronald. Empirical Bayes Estimation of a Binomial Parameter Via Mixtures of Dirichlet Processes. Ann. Statist. 7 (1979), no. 3, 558--568. doi:10.1214/aos/1176344677. https://projecteuclid.org/euclid.aos/1176344677


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