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Trimming and likelihood: Robust location and dispersion estimation in the elliptical model. (English) Zbl 1148.62038
Summary: 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 on 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 \(n^{1/2}\), independently of the rate of convergence of the initial estimator.

62H12 Estimation in multivariate analysis
62F35 Robustness and adaptive procedures (parametric inference)
62F12 Asymptotic properties of parametric estimators
62F10 Point estimation
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