Competitive estimation of the extreme value index

The mean-of-order  -pp (MOp) extreme value index   (EVI) estimators are based on Hölder’s mean of an adequate set of statistics, and generalize the classical Hill EVI-estimators, associated with p=0p=0. Such a class of estimators, dependent on the tuning parameter p∈Rp∈R, has revealed to be highly flexible, but it is not invariant for changes in location. To make the MOpp location-invariant, it is thus sensible to use the peaks over a random threshold   (PORT) methodology, based upon the excesses over an adequate ascending order statistic. In this article, apart from an asymptotic comparison at optimal levels of the optimal MOpp class and some competitive EVI-estimators, like a Pareto probability weighted moments EVI-estimator, a few details on PORT classes of EVI-estimators are provided, enhancing their high efficiency both asymptotically and for finite samples.