On the asymptotic normality of Hill's estimator of the tail index under random censoring

The classical Hill estimator is the most popular estimator of the extreme value index of Pareto-type distributions in the case of complete data. Einmahl, Fils-Villetard and Guillou (2008, Bernoulli 14, no. 1, 207-227) adjusted this estimator (amongst others) to the case where the data are subject to random censorship. They established its asymptotic normality under some restrictive conditions. In this paper, we relax these conditions and represent the adapted estimator in terms of Brownian bridges. Keywords: Brownian bridges; Extreme value index; Heavy-tailed distributions; Hill estimator; Random censoring.