Nelson-Aalen kernel estimator to the tail index of right censored Pareto-type data
Statistics Theory
2025-06-24 v2 Statistics Theory
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.
Cite
@article{arxiv.2505.09152,
title = {Nelson-Aalen kernel estimator to the tail index of right censored Pareto-type data},
author = {Nour Elhouda Guesmia and Abdelhakim Necir and Djamel Meraghni},
journal= {arXiv preprint arXiv:2505.09152},
year = {2025}
}