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Yet another breakdown point notion: EFSBP

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  • Peter Ruckdeschel

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  • Nataliya Horbenko

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    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

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    File URL: http://hdl.handle.net/10.1007/s00184-011-0366-4
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    Bibliographic Info

    Article provided by Springer in its journal Metrika.

    Volume (Year): 75 (2012)
    Issue (Month): 8 (November)
    Pages: 1025-1047

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    Handle: RePEc:spr:metrik:v:75:y:2012:i:8:p:1025-1047

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    Web page: http://www.springerlink.com/link.asp?id=102509

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    Related research

    Keywords: Global robustness; Finite sample breakdown point; Partial equivariance; Scale-shape parametric family; LD estimator;

    References

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