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Yet another breakdown point notion: EFSBP

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  • Peter Ruckdeschel
  • Nataliya Horbenko

Abstract

The breakdown point in its different variants is one of the central notions to quantify the global robustness of a procedure. We propose a simple supplementary variant which is useful in situations where we have no obvious or only partial equivariance: Extending the Donoho and Huber (The notion of breakdown point, Wadsworth, Belmont, 1983 ) Finite Sample Breakdown Point , we propose the Expected Finite Sample Breakdown Point to produce less configuration-dependent values while still preserving the finite sample aspect of the former definition. We apply this notion for joint estimation of scale and shape (with only scale-equivariance available), exemplified for generalized Pareto, generalized extreme value, Weibull, and Gamma distributions. In these settings, we are interested in highly-robust, easy-to-compute initial estimators; to this end we study Pickands-type and Location-Dispersion-type estimators and compute their respective breakdown points. Copyright Springer-Verlag 2012

Suggested Citation

  • Peter Ruckdeschel & Nataliya Horbenko, 2012. "Yet another breakdown point notion: EFSBP," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(8), pages 1025-1047, November.
    • Handle: RePEc:spr:metrik:v:75:y:2012:i:8:p:1025-1047
    DOI: 10.1007/s00184-011-0366-4
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    References listed on IDEAS

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    1. Marazzi, A. & Ruffieux, C., 1999. "The truncated mean of an asymmetric distribution," Computational Statistics & Data Analysis, Elsevier, vol. 32(1), pages 79-100, November.
    2. Ruckdeschel, Peter & Rieder, Helmut, 2010. "Fisher information of scale," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1881-1885, December.
    3. Kris Boudt & Derya Caliskan & Christophe Croux, 2011. "Robust explicit estimators of Weibull parameters," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 73(2), pages 187-209, March.
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    Cited by:

    1. Tino Werner, 2023. "Quantitative robustness of instance ranking problems," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(2), pages 335-368, April.

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