Consider a distribution function that belongs to the weak domain of attraction of an extreme value distribution. The extreme value index $\beta$ will be estimated by mixtures of Pickands estimators, where the weights are generated by a probability measure which satisfies a certain integrability condition. We prove a functional limit theorem for a process of Pickands estimators and asymptotic normality of the refined Pickands estimator. For negative $\beta$ the new estimator is asymptotically superior to previously defined estimators. A simulation study also demonstrates the good small-sample performance. In particular, the estimator proves to be robust against an inappropriate choice of the number of upper order statistics used for estimation.
"Refined Pickands estimators of the extreme value index." Ann. Statist. 23 (6) 2059 - 2080, December 1995. https://doi.org/10.1214/aos/1034713647