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

TL;DR

This paper introduces a new kernel estimator for the tail index of right-censored Pareto-like data, demonstrating improved bias and stability over existing methods through theoretical analysis and simulation, with practical application to insurance data.

Contribution

A novel kernel estimator for the tail index based on Nelson-Aalen estimator, with proven consistency and asymptotic normality under regularity conditions.

Findings

Estimator outperforms existing methods in bias and stability

Simulation confirms improved performance with slight increase in MSE

Applied successfully to insurance loss data

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.