A Lynden-Bell integral estimator for the tail index of right-truncated data with a random threshold

摘要

By means of a Lynden-Bell integral with deterministic threshold, Worms andWorms [A Lynden-Bell integral estimator for extremes of randomly truncateddata. Statist. Probab. Lett. 2016; 109: 106-117] recently introduced anasymptotically normal estimator of the tail index for randomly right-truncatedPareto-type data. In this context, we consider the random threshold case toderive a Hill-type estimator and establish its consistency and asymptoticnormality. A simulation study is carried out to evaluate the finite samplebehavior of the proposed estimator.