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Convergence of the optimal M-estimator over a parametric family of M-estimators

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Abstract

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.

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  1. Department of Mathematical Sciences, Binghamton University, 13902, Binghamton, NY, USA

    Miguel A. Arcones

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  1. Miguel A. Arcones
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Correspondence to Miguel A. Arcones.

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Arcones, M.A. Convergence of the optimal M-estimator over a parametric family of M-estimators. Test 14, 281–315 (2005). https://doi.org/10.1007/BF02595407

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  • DOI: https://doi.org/10.1007/BF02595407

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