Nelson-Aalen Tail Product-limit Process and Extreme Value Index Estimation Under Random Censorship

Djamel Meraghni (), Abdelhakim Necir () and Louiza Soltane ()
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Djamel Meraghni: Mohamed Khider University
Abdelhakim Necir: Mohamed Khider University
Louiza Soltane: Mohamed Khider University

Sankhya A: The Indian Journal of Statistics, 2025, vol. 87, issue 2, No 9, 526-574

Abstract: Abstract On the basis of Nelson-Aalen nonparametric estimator of the cumulative distribution function, we provide a weak approximation to tail product-limit process for randomly right-censored heavy-tailed data. In this context, a new consistent estimator of the extreme value index is introduced and its asymptotic normality is established only by assuming the second-order condition of regular variation of the underlying distribution tail. In addition, an estimation procedure is described for high quantiles related to the above-mentioned tail index estimator. Finally, a simulation study is carried out to evaluate the performances of the newly proposed estimators with comparison to already existing ones.

Keywords: Extreme values; Heavy tails; Hill estimator; Nelson-Aalen estimator; Random censoring; Tail index; 62P05; 62H20; 91B26; 91B30 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s13171-025-00384-y

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