A simulation study of invariant second-order reduced-bias Extreme value index estimators

In this paper, we deal with corrected-bias estimation of a positive extreme value index (EVI), the primary parameter in Statistics of Extremes. Under this context, the classical EVI-estimators are the Hill estimators, based on an intermediate number k of top order statistics. But the Hill estimators are not location-invariant, contrarily to the PORT-Hill estimators, which depend on an extra tuning parameter q, with 0 ≤ q <; 1. On the basis of second-order minimum-variance reduced-bias (MVRB) EVI-estimators, we shall here consider and study, through Monte-Carlo simulation, the new PORT-MVRB EVI-estimators.