Properties of Estimators in the Regular Case

Abstract

In the preceding chapter, some general properties of estimators in the case when the family of distributions obeys the LAN property were established. In particular, a minimax lower bound on the quality of various estimates for a large class of loss functions were derived. The main purpose of the present chapter is to prove the asymptotic efficiency of a maximum likelihood estimator and of a large class of Bayesian and generalized Bayesian estimators for regular families of experiments. Evidently, certain new restrictions on the families under consideration will be required.