Empirical Bayes Estimators and EM Algorithms in One-Way Analysis of Variance Situations

Abstract

The thesis of this paper is two-fold, namely that when there is a choice of working with a joint posterior or a marginal posterior, there may be an optimal choice of which posterior to use, so that care must be taken as to which posterior to work with, and, secondly, if using the EM algorithm for producing estimators, care must be taken with the choice of parameters to be declared “missing”, for the wrong choice could lead to inconsistent estimators and/or estimators with poor mean square error behavior. These two propositions are exhibited for well defined hierarchical models in this paper. The indication that a choice of which posteriors to work with should be considered, was first made by (1976), and this is further discussed in (1996).