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.
Publié le : 1979-05-14
Classification:
Empirical Bayes estimation,
Dirichlet processes,
mixtures of Dirichlet processes,
approximating mixtures of Dirichlet processes,
binomial parameter estimation,
62C10,
62F15,
62F10
@article{1176344677,
author = {Berry, Donald A. and Christensen, Ronald},
title = {Empirical Bayes Estimation of a Binomial Parameter Via Mixtures of Dirichlet Processes},
journal = {Ann. Statist.},
volume = {7},
number = {1},
year = {1979},
pages = { 558-568},
language = {en},
url = {http://dml.mathdoc.fr/item/1176344677}
}
Berry, Donald A.; Christensen, Ronald. Empirical Bayes Estimation of a Binomial Parameter Via Mixtures of Dirichlet Processes. Ann. Statist., Tome 7 (1979) no. 1, pp. 558-568. http://gdmltest.u-ga.fr/item/1176344677/