Adaptive PORT-MVRB estimation: an empirical comparison of two heuristic algorithms

Abstract

In this article, we deal with an empirical comparison of two data-driven heuristic procedures of estimation of a positive extreme value index (EVI), working thus with heavy right tails. The semi-parametric EVI-estimators under consideration, the so-called peaks over random threshold (PORT)-minimum-variance reduced-bias (MVRB) EVI-estimators, are location and scale-invariant estimators, based on the PORT methodology applied to second-order MVRB EVI-estimators. Trivial adaptations of these algorithms make them work for a similar estimation of other parameters of extreme events, such as the Value-at-Risk at a level p, the expected shortfall and the probability of exceedance of a high level x, among others. Applications to simulated data sets and to real data sets in the field of finance are provided. © 2013 Copyright Taylor and Francis Group, LLC.