Optimal robust M-estimators using Rényi pseudodistances

Authors:
Aida Toma;Samuela Leoni-Aubin
Affiliations:
Department of Applied Mathematics, Bucharest Academy of Economic Studies, Piaa Roman 6, Bucharest, Romania and "Gheorghe Mihoc - Caius Iacob" Institute of Mathematical Statistics and Applied Mathe ...;INSA Lyon, ICJ, 20, Rue Albert Einstein, 69621 Villeurbanne Cedex, France
Venue:
Journal of Multivariate Analysis
Year:
2013

Citing 3
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Abstract

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"""@a-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.