Consider an experiment yielding an observable random quantity X
whose distribution Fθ
depends on a parameter θ
with θ being distributed according to some distribution
G0. We study the Bayesian estimation problem of θ
under squared error loss function based on X, 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 θ 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 X 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.
