Nelson-Aalen tail product-limit process and extreme value index estimation under random censorship

Brahim Brahimi; Djamel Meraghni; Abdelhakim Necir

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arXiv · 1502.03955

Nelson-Aalen tail product-limit process and extreme value index estimation under random censorship

Brahim Brahimi·Djamel Meraghni·Abdelhakim Necir

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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 reduced-bias estimator of the extreme value index is introduced and its asymptotic normality is established only by assuming the second-order regular variation of the underlying distribution function. A simulation study shows that the newly proposed estimator performs better than the existing ones.

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Brahim Brahimi, Djamel Meraghni, Abdelhakim Necir. 2015-02-13. Nelson-Aalen tail product-limit process and extreme value index estimation under random censorship. https://arxiv.org/abs/1502.03955

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