Jackknife methodology for bias reduction in tail index estimation under random truncation

Abstract

This paper introduces a novel family of tail index estimators designed to reduce bias and improve the asymptotic properties of existing estimators within the framework of extreme value theory. The focus is specifically on estimating the extreme value index, γ₁, under a random right-truncation model where observations are drawn from heavy-tailed distributions. Using a generalized Jackknife methodology, the proposed estimators are demonstrated to exhibit asymptotic normality, a key property for valid statistical inference on the tail index. Comprehensive simulation studies, including those based on Burr distributions, demonstrate that these new estimators significantly outperform traditional methods, such as Hill-type estimators, in terms of both asymptotic absolute bias and absolute mean squared error. These findings indicate that the generalized Jackknife approach provides a more robust and reliable method for tail index estimation, particularly in heavy-tailed distributions subject to right truncation. This advancement is critical for enhancing statistical analyses in fields that depend on accurate tail behavior assessments, such as finance, insurance, and risk management.