A new partially reduced-bias mean-of-order pp class of extreme value index estimators

A class of partially reduced-bias estimators of a positive extreme value index   (EVI), related to a mean-of-order-pp class of EVI-estimators, is introduced and studied both asymptotically and for finite samples through a Monte-Carlo simulation study. A comparison between this class and a representative class of minimum-variance reduced-bias (MVRB) EVI-estimators is further considered. The MVRB EVI-estimators are related to a direct removal of the dominant component of the bias of a classical estimator of a positive EVI, the Hill estimator, attaining as well minimal asymptotic variance. Heuristic choices for the tuning   parameters pp and kk, the number of top order statistics used in the estimation, are put forward, and applied to simulated and real data.