Kernel estimation for the tail index of a right-censored Pareto-type distribution

TL;DR

This paper proposes a new kernel estimator for the tail index of right-censored Pareto-type distributions, improving smoothness and bias reduction over previous methods, with theoretical and simulation validation.

Contribution

It introduces a generalized kernel estimator for the tail index, including an asymptotically bias-reduced version, enhancing smoothness and accuracy in tail index estimation.

Findings

The kernel estimator is smoother than previous methods.

Bias significantly decreases with the new estimator.

Simulation confirms improved performance with slight MSE increase.

Abstract

We introduce a kernel estimator, to the tail index of a right-censored Pareto-type distribution, that generalizes Worms's one (Worms and Worms, 2014)in terms of weight coefficients. Under some regularity conditions, the asymptotic normality of the proposed estimator is established. In the framework of the second-order condition, we derive an asymptotically bias-reduced version to the new estimator. Through a simulation study, we conclude that one of the main features of the proposed kernel estimator is its smoothness contrary to Worms's one, which behaves, rather erratically, as a function of the number of largest extreme values. As expected, the bias significantly decreases compared to that of the non-smoothed estimator with however a slight increase in the mean squared error.