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Robust Estimators are Hard to Compute

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  • Bernholt, Thorsten

Abstract

In modern statistics, the robust estimation of parameters of a regression hyperplane is a central problem. Robustness means that the estimation is not or only slightly affected by outliers in the data. In this paper, it is shown that the following robust estimators are hard to compute: LMS, LQS, LTS, LTA, MCD, MVE, Constrained M estimator, Projection Depth (PD) and Stahel-Donoho. In addition, a data set is presented such that the ltsReg-procedure of R has probability less than 0.0001 of finding a correct answer. Furthermore, it is described, how to design new robust estimators.

Suggested Citation

  • Bernholt, Thorsten, 2006. "Robust Estimators are Hard to Compute," Technical Reports 2005,52, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    • Handle: RePEc:zbw:sfb475:200552
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    References listed on IDEAS

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    1. Hawkins, Douglas M. & Olive, David, 1999. "Applications and algorithms for least trimmed sum of absolute deviations regression," Computational Statistics & Data Analysis, Elsevier, vol. 32(2), pages 119-134, 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.
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    Cited by:

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    2. Luca Insolia & Ana Kenney & Francesca Chiaromonte & Giovanni Felici, 2022. "Simultaneous feature selection and outlier detection with optimality guarantees," Biometrics, The International Biometric Society, vol. 78(4), pages 1592-1603, December.

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