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 us to relax the assumptionsmade in Einmahl et al. (2008) on the heavy-tailed distribution functions and the sample fraction of upper order statistics.
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Brahimi, B., Meraghni, D. & Necir, A. Gaussian approximation to the extreme value index estimator of a heavy-tailed distribution under random censoring. Math. Meth. Stat. 24, 266–279 (2015). https://doi.org/10.3103/S106653071504002X
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DOI: https://doi.org/10.3103/S106653071504002X