Yet another breakdown point notion: EFSBP - illustrated at scale-shape models

Details Yet another breakdown point notion: EFSBP - illustrated at scale-shape models Yet another breakdown point notion: EFSBP - illustrated at scale-shape models

2010-05-10

arxiv.org/abs/1005.1480v3

Statistics

Methodology

21 pages, 4 figures

Scientific paper

10.1007/s00184-011-0366-4

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(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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