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Yet another breakdown point notion: EFSBP

Illustrated at scale-shape models

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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.

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Authors and Affiliations

  1. Department of Financial Mathematics, Fraunhofer ITWM, Fraunhofer-Platz 1, 67663, Kaiserslautern, Germany

    Peter Ruckdeschel & Nataliya Horbenko

  2. Department of Mathematics, University of Kaiserslautern, P.O. Box 3049, 67653, Kaiserslautern, Germany

    Nataliya Horbenko

Authors
  1. Peter Ruckdeschel
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  2. Nataliya Horbenko
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Correspondence to Peter Ruckdeschel.

Additional information

This work was supported by a DAAD scholarship for N.H.

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Ruckdeschel, P., Horbenko, N. Yet another breakdown point notion: EFSBP. Metrika 75, 1025–1047 (2012). https://doi.org/10.1007/s00184-011-0366-4

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  • DOI: https://doi.org/10.1007/s00184-011-0366-4

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