Gaussian approximation to the extreme value index estimator of a heavy-tailed distribution under random censoring

Abstract

We make use of the empirical process theory to approximate the adapted Hill estimator, for censored data, in terms of Gaussian processes. Then, we derive its asymptotic normality, only under the usual second-order condition of regular variation. Our methodology allows to relax the assumptions, made in Einmahl, Fils-Villetard and Guillou(2008), on the heavy-tailed distribution functions and the sample fraction of upper order statistics.