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The influence function of the Stahel-Donoho covariance estimator of smallest outlyingness

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  • Debruyne, M.
  • Hubert, M.

Abstract

In traditional multivariate location and scatter estimation based on the Stahel-Donoho outlyingness, a weight function is applied, usually calibrated with respect to the multivariate Gaussian distribution. Other robust methods compute the covariance matrix of a fixed size subset of the data (e.g. the MCD estimator). In this paper we study a combination of both the ideas. Location and scatter are estimated using a fixed size subset of the data containing the points with smallest Stahel-Donoho outlyingness. Local robustness and asymptotic relative efficiency are investigated.

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  • Debruyne, M. & Hubert, M., 2009. "The influence function of the Stahel-Donoho covariance estimator of smallest outlyingness," Statistics & Probability Letters, Elsevier, vol. 79(3), pages 275-282, February.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:3:p:275-282
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    References listed on IDEAS

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    1. Hengjian Cui, 2003. "Asymptotic distributions of principal components based on robust dispersions," Biometrika, Biometrika Trust, vol. 90(4), pages 953-966, December.
    2. Gervini, Daniel, 2002. "The influence function of the Stahel-Donoho estimator of multivariate location and scatter," Statistics & Probability Letters, Elsevier, vol. 60(4), pages 425-435, December.
    3. Croux, Christophe & Haesbroeck, Gentiane, 1999. "Influence Function and Efficiency of the Minimum Covariance Determinant Scatter Matrix Estimator," Journal of Multivariate Analysis, Elsevier, vol. 71(2), pages 161-190, November.
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    Cited by:

    1. M. Hubert & P. Rousseeuw & K. Vakili, 2014. "Shape bias of robust covariance estimators: an empirical study," Statistical Papers, Springer, vol. 55(1), pages 15-28, February.
    2. Van Aelst, S. & Vandervieren, E. & Willems, G., 2012. "A Stahel–Donoho estimator based on huberized outlyingness," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 531-542.
    3. Serneels, Sven & Verdonck, Tim, 2009. "Principal component regression for data containing outliers and missing elements," Computational Statistics & Data Analysis, Elsevier, vol. 53(11), pages 3855-3863, September.

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