🤖 AI Summary
This study addresses the bias inherent in tail index estimation for heavy-tailed distributions by proposing a novel estimator that integrates bias correction with empirical likelihood. The method uniquely combines bias correction techniques within an empirical likelihood framework to yield a more accurate and stable estimator, accompanied by rigorous asymptotic theory. Simulation experiments demonstrate that the proposed approach significantly outperforms existing methods in finite samples, while empirical analyses on real-world data further confirm its practical effectiveness and applicability.
📝 Abstract
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.