Robust Estimation by Means of Scaled Bregman Power Distances. Part II. Extreme Values

Abstract

In the separate Part I (see [23]), we have derived a new robustness-featured parameter-estimation framework, in terms of minimization of the scaled Bregman power distances of Stummer and Vajda [25] (see also [24]); this leads to a wide range of outlier-robust alternatives to the omnipresent non-robust method of maximum-likelihood-examination. In the current Part II, we provide some applications of our framework to data from potentially rare but dangerous events (modeled with approximate extreme value distributions), by estimating the correspondingly characterizing extreme value index (reciprocal of tail index); as a special subcase, we recover the method of Ghosh [9] which is essentially a robustification of the procedure of Matthys and Beirlant [19]. Some simulation studies demonstrate the potential partial superiority of our method.