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A Stahel–Donoho estimator based on huberized outlyingness

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  • Van Aelst, S.
  • Vandervieren, E.
  • Willems, G.

Abstract

The Stahel–Donoho estimator is defined as a weighted mean and covariance, where the weight of each observation depends on a measure of its outlyingness. In high dimensions, it can easily happen that a number of outlying measurements are present in such a way that the majority of observations are contaminated in at least one of their components. In these situations, the Stahel–Donoho estimator has difficulties in identifying the actual outlyingness of the contaminated observations. An adaptation of the Stahel–Donoho estimator is presented in which the data are huberized before the outlyingness is computed. It is shown that the huberized outlyingness better reflects the actual outlyingness of each observation towards the non-contaminated observations. Therefore, the resulting adapted Stahel–Donoho estimator can better withstand large numbers of outliers. It is demonstrated that the Stahel–Donoho estimator based on huberized outlyingness works especially well when the data are heavily contaminated.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:3:p:531-542
    DOI: 10.1016/j.csda.2011.08.014
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    References listed on IDEAS

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    1. Cerioli, Andrea & Farcomeni, Alessio, 2011. "Error rates for multivariate outlier detection," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 544-553, January.
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    Cited by:

    1. Cerioli, Andrea & Farcomeni, Alessio & Riani, Marco, 2013. "Robust distances for outlier-free goodness-of-fit testing," Computational Statistics & Data Analysis, Elsevier, vol. 65(C), pages 29-45.
    2. Stefan Van Aelst, 2015. "Comments on: Robust estimation of multivariate location and scatter in the presence of cellwise and casewise contamination," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 478-481, September.
    3. Stefan Aelst & Ruben H. Zamar, 2019. "Comments on: Data science, big data and statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 360-362, June.
    4. Leung, Andy & Yohai, Victor & Zamar, Ruben, 2017. "Multivariate location and scatter matrix estimation under cellwise and casewise contamination," Computational Statistics & Data Analysis, Elsevier, vol. 111(C), pages 59-76.
    5. Claudio Agostinelli & Andy Leung & Victor Yohai & Ruben Zamar, 2015. "Robust estimation of multivariate location and scatter in the presence of cellwise and casewise contamination," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 441-461, September.
    6. Stephane Heritier & Maria-Pia Victoria-Feser, 2018. "Discussion of “The power of monitoring: how to make the most of a contaminated multivariate sample” by Andrea Cerioli, Marco Riani, Anthony C. Atkinson and Aldo Corbellini," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(4), pages 595-602, December.
    7. Tarr, G. & Müller, S. & Weber, N.C., 2016. "Robust estimation of precision matrices under cellwise contamination," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 404-420.
    8. Cerioli, Andrea & Farcomeni, Alessio & Riani, Marco, 2014. "Strong consistency and robustness of the Forward Search estimator of multivariate location and scatter," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 167-183.

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