Multivariate generalized S-estimators

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 cas...

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Bibliographic Details
Published in:Journal of multivariate analysis 2009-05, Vol.100 (5), p.876-887
Main Authors: Roelant, E., Van Aelst, S., Croux, C.
Format: Article
Language:English
Subjects:
62F35
62F40
62F40 62F35 62J05 Bootstrap Efficiency Multivariate regression Robustness
62J05
Bootstrap
Bootstrap method
Efficiency
Estimating techniques
Exact sciences and technology
Linear inference, regression
Mathematics
Matrix
Multivariate analysis
Multivariate regression
Nonparametric inference
Parametric inference
Probability and statistics
Regression analysis
Robustness
Sciences and techniques of general use
Statistics
Studies
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Summary: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.
ISSN:0047-259X
1095-7243
DOI:10.1016/j.jmva.2008.09.002