Title: Peaks-Over-Threshold Modeling Under Random Censoring
Authors: Beirlant, Jan ×
Guillou, Armelle
Toulemonde, Gwladys #
Issue Date: 2010
Publisher: Marcel Dekker
Series Title: Communications in Statistics: Theory and Methods vol:39 issue:7 pages:1158-1179
Abstract: Recently, the topic of extreme value under random censoring has been considered. Different estimators for the index have been proposed (see Beirlant et al., 2007). All of them are constructed as the classical estimators (without censoring) divided by the proportion of non censored observations above a certain threshold. Their asymptotic normality was established by Einmahl et al. (2008). An alternative approach consists of using the Peaks-Over-Threshold method (Balkema and de Haan, 1974; Smith, 1987) and to adapt the likelihood to the context of censoring. This leads to ML-estimators whose asymptotic properties are still unknown. The aim of this article is to propose one-step approximations, based on the Newton-Raphson algorithm. Based on a small simulation study, the one-step estimators are shown to be close approximations to the ML-estimators. Also, the asymptotic normality of the one-step estimators has been established, whereas in case of the ML-estimators it is still an open problem. The proof of our result, whose approach is new in the Peaks-Over-Threshold context, is in the spirit of Lehmann's theory (1991).
ISSN: 0361-0926
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Non-KU Leuven Association publications
× corresponding author
# (joint) last author

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