Open Access
October 2008 Trimming and likelihood: Robust location and dispersion estimation in the elliptical model
Juan A. Cuesta-Albertos, Carlos Matrán, Agustín Mayo-Iscar
Ann. Statist. 36(5): 2284-2318 (October 2008). DOI: 10.1214/07-AOS541


Robust estimators of location and dispersion are often used in the elliptical model to obtain an uncontaminated and highly representative subsample by trimming the data outside an ellipsoid based in the associated Mahalanobis distance. Here we analyze some one (or k)-step Maximum Likelihood Estimators computed on a subsample obtained with such a procedure.

We introduce different models which arise naturally from the ways in which the discarded data can be treated, leading to truncated or censored likelihoods, as well as to a likelihood based on an only outliers gross errors model. Results on existence, uniqueness, robustness and asymptotic properties of the proposed estimators are included. A remarkable fact is that the proposed estimators generally keep the breakdown point of the initial (robust) estimators, but they could improve the rate of convergence of the initial estimator because our estimators always converge at rate n1/2, independently of the rate of convergence of the initial estimator.


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Juan A. Cuesta-Albertos. Carlos Matrán. Agustín Mayo-Iscar. "Trimming and likelihood: Robust location and dispersion estimation in the elliptical model." Ann. Statist. 36 (5) 2284 - 2318, October 2008.


Published: October 2008
First available in Project Euclid: 13 October 2008

zbMATH: 1148.62038
MathSciNet: MR2458188
Digital Object Identifier: 10.1214/07-AOS541

Primary: 62F35
Secondary: 62F10 , 62F12

Keywords: asymptotics , Breakdown point , censored maximum likelihood , elliptical distributions , exponential family , gross errors model , Identifiability , multivariate normal distribution , MVE estimator , smart estimator , truncated maximum likelihood

Rights: Copyright © 2008 Institute of Mathematical Statistics

Vol.36 • No. 5 • October 2008
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