A Bias-reduced Estimator for the Mean of a Heavy-tailed Distribution with an Infinite Second Moment

TL;DR

This paper introduces a new bias-reduced estimator for the mean of heavy-tailed distributions with infinite variance, demonstrating its asymptotic normality and superior performance over existing estimators through simulations.

Contribution

It proposes a novel mean estimator leveraging bias-reduced high quantile estimators specifically for heavy-tailed distributions with infinite second moments.

Findings

Estimator is asymptotically normal.

Outperforms Peng's estimator in bias and MSE.

Provides accurate confidence intervals.

Abstract

We use bias-reduced estimators of high quantiles, of heavy-tailed distributions, to introduce a new estimator of the mean in the case of infinite second moment. The asymptotic normality of the proposed estimator is established and checked, in a simulation study, by four of the most popular goodness-of-fit tests for different sample sizes. Moreover, we compare, in terms of bias and mean squared error, our estimator with Peng's estimator (Peng, 2001) and we evaluate the accuracy of some resulting confidence intervals.