On asymptotic optimality of estimators of parameters under the LAQ condition

In this paper we consider the problem of asymptotic optimality of estimators of parameters under the local asymptotic quadratic condition. It is shown that if the deviation of estimators from the true value is normed by a specially chosen random factor, then the so-called asymptotically centered estimators are asymptotically admissible for the quadratic loss function and have the smallest asymptotic variance among estimators with an asymptotically constant bias.