On a predictive measure of discrepancy between classical and Bayesian estimators

In the presence of prior information on an unknown parameter of a statis- tical model, Bayesian and frequentist estimates based on the same observed data do not coincide. However it is well known that, in many standard parametric problems, their discrepancy tends to be reduced as the sample size increases. In this paper we consider a measure of discrepancy, Dn, between a frequentist and a Bayesian point estimator and we study its predictive distribution. In some specific examples we an- alyze the main characteristics of this predictive distribution for increasing sample sizes. We also consider the use of the predictive density of Dn for the assessment of a prior distribution informativeness. Some explicit results are given for the normal model.