The multivariate least-trimmed squares estimator

Authors:
Jose Agulló;Christophe Croux;Stefan Van Aelst
Affiliations:
Departamento de Fundamentos del Análisis Económico, University of Alicante, E-03080, Alicante, Spain;Faculty of Economics and Applied Economics, ORSTAT Research Center, KU Leuven, Naamsestraat 69, B-3000 Leuven, Belgium;Department of Applied Mathematics and Computer Science, Ghent University (UGENT), Krijgslaan 281 S9, B-9000 Gent, Belgium
Venue:
Journal of Multivariate Analysis
Year:
2008

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Abstract

In this paper we introduce the least-trimmed squares estimator for multivariate regression. We give three equivalent formulations of the estimator and obtain its breakdown point. A fast algorithm for its computation is proposed. We prove Fisher-consistency at the multivariate regression model with elliptically symmetric error distribution and derive the influence function. Simulations investigate the finite-sample efficiency and robustness of the estimator. To increase the efficiency of the estimator, we also consider a one-step reweighted estimator.