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Tail product-limit process for truncated data with application to extreme value index estimation

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Abstract

A weighted Gaussian approximation to tail product-limit process for Pareto-like distributions of randomly right-truncated data is provided and a new consistent and asymptotically normal estimator of the extreme value index is introduced. A simulation study is carried out to evaluate the finite sample behavior of the proposed estimator and compare it to that recently proposed by Gardes and Stupfler (TEST 24, 207–227, 2015). Also, a new approach of estimating extreme quantiles, under random right truncation, is derived and applied to a real dataset of lifetimes of automobile brake pads.

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Authors and Affiliations

  1. Laboratory of Applied Mathematics, Mohamed Khider University, Biskra, Algeria

    Souad Benchaira, Djamel Meraghni & Abdelhakim Necir

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  1. Souad Benchaira
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  2. Djamel Meraghni
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  3. Abdelhakim Necir
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Correspondence to Abdelhakim Necir.

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Benchaira, S., Meraghni, D. & Necir, A. Tail product-limit process for truncated data with application to extreme value index estimation. Extremes 19, 219–251 (2016). https://doi.org/10.1007/s10687-016-0241-9

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  • DOI: https://doi.org/10.1007/s10687-016-0241-9

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