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<p>Based on Nelson-Aalen product-limit estimator for randomly right-censored data, we propose a kernel-based estimator to the tail index of Pareto-type distributions under censoring. Under suitable regularity conditions, we establish its consistency and asymptotic normality. A simulation study shows that the smoothed estimator outperforms the non-smoothed version in terms of stability, bias, and mean squared error (MSE). Finally, an application to insurance loss data illustrates the practical usefulness of the method.</p>

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Nelson-Aalen kernel estimator to the tail index of right censored Pareto-type data

  • 期刊论文

  • 发表日期：

    2026年1月9日

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

摘要

Based on Nelson-Aalen product-limit estimator for randomly right-censored data, we propose a kernel-based estimator to the tail index of Pareto-type distributions under censoring. Under suitable regularity conditions, we establish its consistency and asymptotic normality. A simulation study shows that the smoothed estimator outperforms the non-smoothed version in terms of stability, bias, and mean squared error (MSE). Finally, an application to insurance loss data illustrates the practical usefulness of the method.