Author:

Keywords:

bootstrap, efficiency, multivariate regression, robustness

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 independency 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 a symptotically and a finite samples. To obtain inference for the regression parameters, we discuss the fast and robust boot strap for multivariate generalized S-estimators. The method is illustrated on several real data examples.