Improving extreme value statistics

TL;DR

This paper introduces a simple nonlinear transformation technique that significantly improves the convergence and accuracy of extreme value statistics, especially in the tail, with minimal additional computational cost.

Contribution

The authors propose a novel nonlinear transformation approach that enhances the convergence and tail accuracy of extreme value analysis, generalizing classical methods.

Findings

Rapid convergence in the bulk of data

Asymptotic accuracy in the tail

Classical methods as special cases

Abstract

The rate of uniform convergence in extreme value statistics is non-universal and can be arbitrarily slow. Further, the relative error can be unbounded in the tail of the approximation, leading to difficulty in extrapolating the extreme value fit beyond the available data. We show that by using simple nonlinear transformations the extreme value approximation can be rendered rapidly convergent in the bulk, and asymptotic in the tail, thus fixing both issues. The transformations are often parameterized by just one parameter which can be estimated numerically. The classical extreme value method is shown to be a special case of the proposed method. We demonstrate that vastly improved results can be obtained with almost no extra cost.