Convergence of the Optimal M-Estimator over a Parametric Family of M-Estimators
- Autores: Miguel A. Arcones
- Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 14, Nº. 1, 2005, págs. 281-315
- Idioma: inglés
- DOI: 10.1007/bf02595407
- Enlaces
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Resumen
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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