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The bias of k-step M-estimators

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  • Rousseeuw, Peter J.
  • Croux, Christophe

Abstract

It is well-known that k-step M-estimators can yield a high efficiency without losing the breakdown point of the initial estimator. In this note we derive their bias curves. In the location framework the bias increases only slightly with k, but in the scale case the bias curves change considerably.

Suggested Citation

  • Rousseeuw, Peter J. & Croux, Christophe, 1994. "The bias of k-step M-estimators," Statistics & Probability Letters, Elsevier, vol. 20(5), pages 411-420, August.
  • Handle: RePEc:eee:stapro:v:20:y:1994:i:5:p:411-420
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    Citations

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    Cited by:

    1. Sukru Acitas & Pelin Kasap & Birdal Senoglu & Olcay Arslan, 2013. "One-step M -estimators: Jones and Faddy's skewed t -distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(7), pages 1545-1560, July.
    2. Schlittgen, Rainer & Schwabe, Rainer, 2001. "An alternative definition of the influence function," Statistics & Probability Letters, Elsevier, vol. 51(2), pages 143-153, January.
    3. Cem Haydaroğlu & Bilal Gümüş, 2022. "Fault Detection in Distribution Network with the Cauchy-M Estimate—RVFLN Method," Energies, MDPI, vol. 16(1), pages 1-18, December.
    4. Berrendero, José R. & Zamar, Ruben H., 1999. "Global robustness of location and dispersion estimates," Statistics & Probability Letters, Elsevier, vol. 44(1), pages 63-72, August.
    5. Smirnov, Pavel O. & Shevlyakov, Georgy L., 2014. "Fast highly efficient and robust one-step M-estimators of scale based on Qn," Computational Statistics & Data Analysis, Elsevier, vol. 78(C), pages 153-158.
    6. Croux, Christophe & Haesbroeck, Gentiane, 1999. "Influence Function and Efficiency of the Minimum Covariance Determinant Scatter Matrix Estimator," Journal of Multivariate Analysis, Elsevier, vol. 71(2), pages 161-190, November.
    7. Gather, Ursula & Davies, P. Laurie, 2004. "Robust Statistics," Papers 2004,20, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    8. C. Croux & C. Dehon & A. Yadine, 2010. "The k-step spatial sign covariance matrix," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 4(2), pages 137-150, September.

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