Bayesian estimation of the tail index of a heavy tailed distribution under random censoring

Bayesian 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 for various prior distributions of the tail index and their consistency and asymptotic normality are established. Finitesample properties of the proposed estimators are investigated via simulations. Tail index estimation requires selecting an appropriate threshold for constructing relative excesses. A Monte Carlo procedure is proposed for tackling this issue. Finally, the proposed estimators are illustrated on a medical dataset.