International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 2, Pages 97-107
An improved Bayes empirical Bayes estimator
Department of Mathematical and Statistical Sciences, University of Alberta, Alberta, Edmonton T6G 2G1, Canada
Received 27 September 2001
Copyright © 2003 R. J. Karunamuni and N. G. N. Prasad. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Consider an experiment yielding an observable random quantity
depends on a parameter
with being distributed according to some distribution
. We study the Bayesian estimation problem of
under squared error loss function based on , as well as some
additional data available from other similar experiments
according to an empirical Bayes structure. In a recent paper,
Samaniego and Neath (1996) investigated the questions of whether,
and when, this information can be exploited so as to provide a
better estimate of in the current experiment.
They constructed a Bayes empirical Bayes estimator that
is superior to the original Bayes estimator, based only on the
current observation for sampling situations involving
exponential families-conjugate prior pair. In this paper, we
present an improved Bayes empirical Bayes estimator having a
smaller Bayes risk than that of Samaniego and Neath's estimator.
We further observe that our estimator is superior to the original
Bayes estimator in more general situations than those of the
exponential families-conjugate prior combination.