The tail index parameter of heavy-tailed probability models plays a key role in characterizing the tail decay of the underlying distribution function and is often involved in extrapolation procedures for various extreme value analysis questions. In this paper we revisit the question of tail index estimation and combine the ideas of bias-correction and empirical likelihood estimation to propose an estimator that offers an attractive alternative to some of the existing estimators. We develop an asymptotic theory for the proposed estimator and conduct simulation studies to demonstrate its performance in finite sample situations. The method is also applied to a data example for illustration.

翻译：重尾概率模型的尾指数参数在刻画分布函数尾部衰减特征中起关键作用，常被用于各类极值分析问题中的外推过程。本文重新审视尾指数估计问题，融合偏差校正与经验似然估计的思想，提出了一种兼具优良性质的估计量，为现有估计方法提供了极具竞争力的替代方案。我们建立了所提估计量的渐近理论，并通过仿真研究验证了该估计量在有限样本情形下的表现。为阐明方法实用性，本文还将其应用于实际数据案例。