Lehmer's mean-of-order-p extreme value index estimation: a simulation study and applications

The main objective of extreme value theory is essentially the estimation of quantities related to extreme events. One of its main issues has been the estimation of the extreme value index (EVI), a parameter directly related to the tail weight of the distribution. Here we deal with the semi-parametric estimation of the EVI, for heavy tails. A recent class of EVI-estimators, based on the Lehmer's mean-of-order p (L (Formula presented.)), which generalizes the arithmetic mean, is considered. An asymptotic comparison at optimal levels performed in previous works has revealed the competitiveness of this class of EVI-estimators. A large-scale Monte-Carlo simulation study for finite simulated samples has been here performed, showing the behaviour of L (Formula presented.), as a function of p. A bootstrap adaptive choice of (Formula presented.), where k is the number of upper order statistics used in the estimation, and a second algorithm based on a stability criterion are computationally studied and applied to simulated and real data.