Optimal robust M-estimators using Rényi pseudodistances

Aida Toma and Samuela Leoni-Aubin

Journal of Multivariate Analysis, 2013, vol. 115, issue C, 359-373

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.

Keywords: Optimal robust estimation; Rényi pseudodistance; Weibull distribution (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:115:y:2013:i:c:p:359-373

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DOI: 10.1016/j.jmva.2012.10.003

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