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Optimal robust M-estimators using Rényi pseudodistances

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  • Toma, Aida
  • Leoni-Aubin, Samuela

Abstract

Using Rényi pseudodistances, new robustness and efficiency measures are defined. On the basis of these measures, new optimal robust M-estimators for multidimensional parameters, called optimal BRα-robust M-estimators, are derived using the Hampel’s infinitesimal approach. The classical optimal Bi-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.

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  • Toma, Aida & Leoni-Aubin, Samuela, 2013. "Optimal robust M-estimators using Rényi pseudodistances," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 359-373.
    • Handle: RePEc:eee:jmvana:v:115:y:2013:i:c:p:359-373
    DOI: 10.1016/j.jmva.2012.10.003
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    Cited by:

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    2. Diaa Al Mohamad, 2018. "Towards a better understanding of the dual representation of phi divergences," Statistical Papers, Springer, vol. 59(3), pages 1205-1253, September.

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