Bayesian composite confidence interval for the tail index under randomly right-censored data

TL;DR

This paper develops Bayesian methods for estimating the tail index of heavy-tailed distributions with right-censored data, providing confidence regions that outperform existing methods in simulations and real data applications.

Contribution

It introduces Bayesian composite likelihood estimators for the tail index under censoring and constructs novel confidence regions based on asymptotic properties.

Findings

Proposed confidence regions outperform existing methods in simulations.

Bayesian estimators effectively handle right-censored heavy-tailed data.

Method validated on real datasets with improved accuracy.

Abstract

Bayesian composite likelihood estimation of the tail index of a heavy-tailed distribution is addressed when data are randomly right-censored. Maximum a posteriori and mean posterior estimators are constructed under Jeffrey's prior distribution of the tail index. Based on asymptotic results, some confidence regions (CR) for the tail index are constructed using posterior distribution and log-posterior ratio statistic. The proposed confidence regions are investigated via Finite-sample simulations. Finally, the proposed confidence regions are outperformed through two real datasets