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<p>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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年4月9日

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  • Djamel Meraghni,
  • Abdelhakim Necir,
  • Louiza Soltane

摘要

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.