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The influence function of the Stahel-Donoho estimator of multivariate location and scatter

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  • Gervini, Daniel

Abstract

This article derives the influence function of the Stahel-Donoho estimator of multivariate location and scatter for elliptical distributions. Local robustness and asymptotic relative efficiency are studied. The expressions obtained for the influence functions coincide with those of one-step reweighted estimators.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:60:y:2002:i:4:p:425-435
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    Cited by:

    1. Aida Toma & Samuela Leoni-Aubin, 2015. "Robust Portfolio Optimization Using Pseudodistances," PLOS ONE, Public Library of Science, vol. 10(10), pages 1-26, October.
    2. Bernholt, Thorsten, 2006. "Robust Estimators are Hard to Compute," Technical Reports 2005,52, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    3. Xin Dang & Robert Serfling & Weihua Zhou, 2009. "Influence functions of some depth functions, and application to depth-weighted L-statistics," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(1), pages 49-66.
    4. 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.
    5. 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.
    6. Bianco, Ana & Boente, Graciela & Pires, Ana M. & Rodrigues, Isabel M., 2008. "Robust discrimination under a hierarchy on the scatter matrices," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1332-1357, July.

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