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Multivariate generalized S-estimators

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  • Roelant, E.
  • Van Aelst, S.
  • Croux, C.

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.

Suggested Citation

  • Roelant, E. & Van Aelst, S. & Croux, C., 2009. "Multivariate generalized S-estimators," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 876-887, May.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:5:p:876-887
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    References listed on IDEAS

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    2. Khan, Jafar A. & Van Aelst, Stefan & Zamar, Ruben H., 2010. "Fast robust estimation of prediction error based on resampling," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3121-3130, December.
    3. Ilmonen, Pauliina, 2013. "On asymptotic properties of the scatter matrix based estimates for complex valued independent component analysis," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1219-1226.
    4. Kudraszow, Nadia L. & Maronna, Ricardo A., 2011. "Estimates of MM type for the multivariate linear model," Journal of Multivariate Analysis, Elsevier, vol. 102(9), pages 1280-1292, October.

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