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<p>We propose a robust and smooth estimator for the tail index of Pareto-type distributions, based on a weighted density power divergence. By incorporating a weight function, our approach enhances efficiency in the presence of outliers, providing a robust extension of both weighted least squares and kernel-based tail index estimators. We establish consistency and asymptotic normality of the proposed estimators, and conduct a simulation study to evaluate their finite-sample performance relative to existing methods. Finally, the practical relevance and improved reliability of our approach are illustrated through an application to Danish fire insurance data.</p>

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Robust and smooth estimation of the extreme tail index via weighted minimum density power divergence

  • 期刊论文

  • 发表日期：

    2026年2月28日

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  • Saida Mancer,
  • Abdelhakim Necir,
  • Djamel Meraghni

摘要

We propose a robust and smooth estimator for the tail index of Pareto-type distributions, based on a weighted density power divergence. By incorporating a weight function, our approach enhances efficiency in the presence of outliers, providing a robust extension of both weighted least squares and kernel-based tail index estimators. We establish consistency and asymptotic normality of the proposed estimators, and conduct a simulation study to evaluate their finite-sample performance relative to existing methods. Finally, the practical relevance and improved reliability of our approach are illustrated through an application to Danish fire insurance data.