A tail Kaplan-Meier empirical process with application to extreme-value based estimation under random censoring

In the case of complete data, weak approximations to tail empirical processes for heavy-tailed distributions have been established by many authors. In this paper, we consider the random censoring setting through a tail Kaplan-Meier process and define a new estimator of the extreme value index. Under mild conditions, we establish the asymptotic normality of the proposed estimator and, through a simulation study, we investigate its performance and compare it to the adapted Hill estimator introduced by Einmahl, Fils-Villetard and Guillou, 2008.