Asymptotically Minimum Risk Equivariant Estimators

Abstract

Based on n independent and identically distributed random variables, let Tn be a translation equivariant estimator of the location parameter ??. Also, consider the conventional squared error loss function. Let Cn be the class of all Translation equivariant estimators of ??, and let Ynbe a maximal invariant with respect to the translation group. Then, a convenient way of locating a minimum risk equivariant estimator, say, [Image1.gif]is to find a Tn belonging to the same class, and taking [Image2.gif]This prescription allows us to consider a very broad class of robust translation equivariant estimators and characterize the asymptotic minimum risk estimators in a unified and general way. This, in turn, requires the study of some moment convergence properties of such robust estimators, and this has been thoroughly explored here. (joint work with Jana Jureckova, Charles University, Prague, Czech Republic)