Sensitivity of bayes and empirical bayes estimates

Abstract

The main objective is to investigate the behaviour of Bayes and empirical Bayes confidence intervals for a mean to changes from normality in the specification of either the sampling or prior distributions. To do this the posterior mean and variance are calculated when the prior and sampling distributions are defined by Edgeworth expansions, corrective terms being obtained as functions of the standardized higher cumulants. Comparison with the empirical Bayes estimates, calculated under normal assumptions, gives, in particular, the sensitivity to distributional shape. A correction for errors incurred by the estimation of the prior is briefly considered. The results are illustrated by an application to real data.