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Unconventional features of positive-breakdown estimators

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  • Rousseeuw, Peter J.

Abstract

This paper reviews some aspects of positive-breakdown regression that have been discussed. Apart from efficiency, also some related topics are addressed in order to obtain a broader view. Several unusual aspects are shown to be intimately connected with the exact fit property. It is argued that the latter is not a drawback but an interesting property, which helps to explain why positive-breakdown estimators often succeed at revealing a hidden structure in the data.

Suggested Citation

  • Rousseeuw, Peter J., 1994. "Unconventional features of positive-breakdown estimators," Statistics & Probability Letters, Elsevier, vol. 19(5), pages 417-431, April.
    • Handle: RePEc:eee:stapro:v:19:y:1994:i:5:p:417-431
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    Citations

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    Cited by:

    1. Rousseeuw, Peter J. & Verboven, Sabine, 2002. "Robust estimation in very small samples," Computational Statistics & Data Analysis, Elsevier, vol. 40(4), pages 741-758, October.
    2. Visek, Jan Amos, 2000. "On the diversity of estimates," Computational Statistics & Data Analysis, Elsevier, vol. 34(1), pages 67-89, July.
    3. Vakili, Kaveh & Schmitt, Eric, 2014. "Finding multivariate outliers with FastPCS," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 54-66.
    4. Gervini, Daniel, 2003. "A robust and efficient adaptive reweighted estimator of multivariate location and scatter," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 116-144, January.
    5. Steven P. Ellis, 2000. "Singularity and outliers in linear regression with application to least squares, least squares linear regression," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1-2), pages 121-129.
    6. Jan Víšek, 1996. "Sensitivity analysis of M-estimates," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(3), pages 469-495, September.

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