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Multivariate generalized S-estimators. (English) Zbl 1157.62033

Summary: 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 in 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.

MSC:

62H12 Estimation in multivariate analysis
62F35 Robustness and adaptive procedures (parametric inference)
62J05 Linear regression; mixed models
62F40 Bootstrap, jackknife and other resampling methods

Software:

bootlib; wwcode; FastICA
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Full Text: DOI

References:

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