On the Bayesian Stability in the Empirical Bayesian Approach

Abstract

The empirical Bayesian approach is considered for Bayesian stable families of prior parameter distributions. It is shown that in these cases the derivation of the estimate for the Bayesian decision function is considerably simplified. We consider a generalization of the Deely–Lindley’s Bayesian approach to the problem of empirical Bayesian estimation, and present examples of application of the obtained results.