A Reduced-Bias Weighted least square estimation of the Extreme Value Index

TL;DR

This paper introduces a new reduced-bias estimator for the Extreme Value Index (EVI) in heavy-tailed distributions, improving bias and stability over existing methods through weighted least squares and practical validation.

Contribution

It presents a novel unbiased, consistent, and asymptotically normal estimator of EVI using weighted least squares, with demonstrated finite sample advantages and practical applicability.

Findings

Estimator is unbiased, consistent, and asymptotically normal.

Performs better in bias and MSE compared to existing estimators.

Less sensitive to the number of top-order statistics, aiding tail fraction selection.

Abstract

In this paper, we propose a reduced-bias estimator of the EVI for Pareto-type tails (heavy-tailed) distributions. This is derived using the weighted least squares method. It is shown that the estimator is unbiased, consistent and asymptotically normal under the second-order conditions on the underlying distribution of the data. The finite sample properties of the proposed estimator are studied through a simulation study. The results show that it is competitive to the existing estimators of the extreme value index in terms of bias and Mean Square Error. In addition, it yields estimates of $\gamma>0$ that are less sensitive to the number of top-order statistics, and hence, can be used for selecting an optimal tail fraction. The proposed estimator is further illustrated using practical datasets from pedochemical and insurance.