English

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.

Keywords

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}
}