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<p>We introduce a kernel-based estimator for the extreme value index in the presence of randomly right-censored data, extending the classical adapted Hill estimator. The estimator’s consistency and asymptotic normality are rigorously established. A comprehensive simulation study highlights one of its key advantages: a smooth behavior with respect to the number of upper order statistics, in contrast to the non-kernel estimator, which displays more erratic fluctuations. Additionally, a notable reduction in mean squared error is observed compared with the non-smoothed counterpart. The practical applicability of the method is illustrated through two real datasets: insurance losses (weak censoring) and AIDS survival times (strong censoring).</p>

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Adapted kernel estimator to the tail index of randomly right-censored Pareto-type data

  • 期刊论文

  • 发表日期：

    2026年3月14日

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  • Nour Elhouda Guesmia,
  • Abdelhakim Necir,
  • Djamel Meraghni

摘要

We introduce a kernel-based estimator for the extreme value index in the presence of randomly right-censored data, extending the classical adapted Hill estimator. The estimator’s consistency and asymptotic normality are rigorously established. A comprehensive simulation study highlights one of its key advantages: a smooth behavior with respect to the number of upper order statistics, in contrast to the non-kernel estimator, which displays more erratic fluctuations. Additionally, a notable reduction in mean squared error is observed compared with the non-smoothed counterpart. The practical applicability of the method is illustrated through two real datasets: insurance losses (weak censoring) and AIDS survival times (strong censoring).