A class of Pickands-type estimators for the extreme value index

In this paper we introduce a new class of Pickands-type estimators for the extreme value index. Consistency and asymptotic normality of the estimators are established under suitable regularity conditions. The new estimator uses the same fraction of upper-order statistics as the well-known Pickands estimator, but its asymptotic performance is better by at least 10% if it is chosen in some optimal ways. A simulation study also demonstrates its good finite-sample performance.