B1012
Title: Mean of order $p$ reduced bias estimation of the extreme value index: A computational study
Authors: Frederico Caeiro - NOVA.ID.FCT - Universidade Nova de Lisboa (Portugal) [presenting]
Ivette Gomes - FCiencias.ID, Universidade de Lisboa and CEAUL (Portugal)
Abstract: We deal with the estimation of a positive extreme value index, the shape parameter of the extreme value distribution. The classical Hill estimator can be regarded as the logarithm of the geometric mean, or the logarithm of the mean-of-order-0 of a certain set of statistics. Instead of such a geometric mean, the mean-of-order-$p$ (MOP) of those statistics has been previously considered. We work with recent reduced-bias versions of the MOP generalization of the Hill estimator. Apart from the usual integer parameter $k$, related with the number of top order statistics involved in the estimation, these estimators depend on an the extra real parameter $p$. Bootstrap and heuristic choices of the tuning parameters $p$ and $k$ are put forward, and an application to simulated and real data is performed.
