Optimal robust M-estimators using Renyi pseudodistances

Using Renyi pseudodistances, new robustness and efficiency measures are defined. On the basis of these measures, new optimal robust M-estimators for multidimensional parameters, called optimal B-R alpha -robust M-estimators, are derived using the Hampel's infinitesimal approach. The classical optimal B-i-robust estimator is particularly obtained. It is shown that the new optimal estimators are characterized by equivariance properties: equivariance with respect to reparametrizations, as well as equivariance with respect to transformations of the data set when the model is generated by a group of transformations. The performance of these estimators is illustrated by Monte Carlo simulations in the case of the Weibull distribution, as well as on the basis of real data. (C) 2012 Elsevier Inc. All rights reserved.