Resumen de Convergence of the Optimal M-Estimator over a Parametric Family of M-Estimators

Miguel A. Arcones

• We consider a method to select an optimal M-estimator over a family of M-estimators of a parameter. Assuming that there exists an estimate of the mean square error for each element of this family of estimators, a natural estimator to consider is the M-estimator in the class which minimizes the considered estimates of the mean square errors. It is shown that under regularity conditions, this M-estimator is asymptotically normal and its asymptotic mean square error is equal to the infimum of the asymptotic mean square errors of the M-estimators in the class. We see how this method works in two different situations. In order to tackle the former problem, we present sufficient conditions for the weak convergence of a class of M-estimators.