On the asymptotic normality of the adapted Hill estimator for censored data

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) adapted this estimator (amongst others) to the case where the data are subject to random censorship and established its asymptotic normality under three restrictive assumptions. In this paper, we make use of the empirical process theory to represent the adapted estimator in terms of Brownian bridges and hence derive its asymptotic normality only under the usual second-order condition of regular variation.