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Shape bias of robust covariance estimators: an empirical study

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  • M. Hubert
  • P. Rousseeuw
  • K. Vakili

Abstract

Detecting outliers in a multivariate point cloud is not trivial, especially when dealing with a sizable fraction of contamination. Over time, it has increasingly been recognized that the safest and most feasible approach to exposing outliers starts by computing a highly robust estimator of location and scatter that can withstand a large proportion of contamination. Many such estimators have been proposed in recent years. We will compare the worst-case bias of several prominent robust multivariate estimators by means of simulation. We also propose a new tool to compare robust estimators on real data sets, and illustrate it. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stpapr:v:55:y:2014:i:1:p:15-28
    DOI: 10.1007/s00362-013-0544-8
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    Cited by:

    1. 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.
    2. 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.
    3. Jakob Raymaekers & Peter J. Rousseeuw & Iwein Vranckx, 2018. "Discussion of “The power of monitoring: how to make the most of a contaminated multivariate sample”," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(4), pages 589-594, December.

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