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arXiv · 2505.09152

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

Nour Elhouda Guesmia·Abdelhakim Necir·Djamel Meraghni
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Abstract

On the basis of Nelson-Aalen product-limit estimator of a randomly censored distribution function, we introduce a kernel estimator to the tail index of right-censored Pareto-like data. Under some regularity assumptions, the consistency and asymptotic normality of the proposed estimator are established. A small simulation study shows that the proposed estimator performs much better, in terms of bias and stability, than the existing ones with, a slight increase in the mean squared error. The results are applied to insurance loss data to illustrate the practical effectiveness of our estimator.

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Nour Elhouda Guesmia, Abdelhakim Necir, Djamel Meraghni. 2025-05-14. Nelson-Aalen kernel estimator to the tail index of right censored Pareto-type data. https://arxiv.org/abs/2505.09152

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