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

TL;DR

This paper introduces the Expected Finite Sample Breakdown Point (EFSBP), a new robustness measure for statistical procedures with limited equivariance, and applies it to joint scale-shape estimation for various distributions.

Contribution

It extends the classical breakdown point concept to less equivariant settings and demonstrates its application to robust estimation in scale-shape models.

Findings

EFSBP produces less configuration-dependent robustness values.

Pickands-type and Location-Dispersion estimators have high breakdown points.

Application to generalized Pareto, GEV, Weibull, and Gamma distributions.

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(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.