Multivariate generalized S-estimators

Authors:
E. Roelant;S. Van Aelst;C. Croux
Affiliations:
Department of Applied Mathematics and Computer Science, Ghent University - UGent, Krijgslaan 281-S9, B-9000 Gent, Belgium;Department of Applied Mathematics and Computer Science, Ghent University - UGent, Krijgslaan 281-S9, B-9000 Gent, Belgium;Katholieke Universiteit Leuven, Faculty of Economics and Business and Leuven Statistical Research Centre, Naamsestraat 69, B-3000 Leuven, Belgium
Venue:
Journal of Multivariate Analysis
Year:
2009

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Abstract

In this paper we introduce generalized S-estimators for the multivariate regression model. This class of estimators combines high robustness and high efficiency. They are defined by minimizing the determinant of a robust estimator of the scatter matrix of differences of residuals. In the special case of a multivariate location model, the generalized S-estimator has the important independence property, and can be used for high breakdown estimation in independent component analysis. Robustness properties of the estimators are investigated by deriving their breakdown point and the influence function. We also study the efficiency of the estimators, both asymptotically and at finite samples. To obtain inference for the regression parameters, we discuss the fast and robust bootstrap for multivariate generalized S-estimators. The method is illustrated on a real data example.