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

TL;DR

This paper introduces a kernel estimator for the tail index of a Pareto-type distribution with right-truncation, demonstrating improved bias and mean squared error in small samples through asymptotic analysis and simulations.

Contribution

A novel kernel estimator for the tail index under right-truncation, with proven asymptotic normality and superior small-sample performance.

Findings

Estimator outperforms existing methods in bias and MSE

Asymptotic normality established for the estimator

Simulation results confirm improved accuracy in small samples

Abstract

In this paper, we define a kernel estimator for the tail index of a Pareto-type distribution under random right-truncation and establish its asymptotic normality. A simulation study shows that, compared to the estimators recently proposed by Gardes & Stupfler (2015) and Benchaira et al. (2015), this newly introduced estimator behaves better, in terms of bias and mean squared error, for small samples.