## An improved Bayes empirical Bayes estimator.(English)Zbl 1013.62004

Summary: Consider an experiment yielding an observable random quantity $$X$$ whose distribution $$F_{\theta}$$ depends on a parameter $$\theta$$ with $$\theta$$ being distributed according to some distribution $$G_0$$. We study the Bayesian estimation problem of $$\theta$$ under a 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, F.J. Samaniego and A.A. Neath [J. Am. Stat. Assoc. 91, No. 434, 733-742 (1996; Zbl 0869.62006)] investigated the questions of whether, and when, this information can be exploited so as to provide a better estimate of $$\theta$$ 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 pairs. 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.

### MSC:

 62C12 Empirical decision procedures; empirical Bayes procedures 62F15 Bayesian inference

### Keywords:

numerical example

Zbl 0869.62006
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