Olav Aabakken

Abstract

An empirical linear Bayes estimator is asymptotically optimal in the usual sense if its average risk converges to the risk of the corresponding linear Bayes estimator. The present paper demonstrates that the following result holds for the most commonly used models: If the unknown (structural) parameters are estimated in such a way that their mean square error converges at a certain rate, then the corresponding empirical linear Bayes estimator is asymptotically optimal with the same rate of risk convergence. In particular, this is the case for the random coefficient regression model, and for hierarchical models in the univariate case.