Improved inference on risk measures for univariate extremes

TL;DR

This paper explores advanced likelihood-based methods for more accurate risk measure inference in univariate extreme value analysis, demonstrating robustness and potential improvements in practical applications like rainfall and lifespan studies.

Contribution

It introduces higher-order approximation techniques for extreme value inference, highlighting their advantages and limitations compared to traditional methods.

Findings

Maxima-based inference is robust to mild model misspecification.

Profile likelihood confidence intervals are often sufficient.

Higher-order methods can reduce bias in threshold exceedance analysis.

Abstract

We discuss the use of likelihood asymptotics for inference on risk measures in univariate extreme value problems, focusing on estimation of high quantiles and similar summaries of risk for uncertainty quantification. We study whether higher-order approximation based on the tangent exponential model can provide improved inferences, and conclude that inference based on maxima is generally robust to mild model misspecification and that profile likelihood-based confidence intervals will often be adequate, whereas inferences based on threshold exceedances can be badly biased but may be improved by higher-order methods, at least for moderate sample sizes. We use the methods to shed light on catastrophic rainfall in Venezuela, flooding in Venice, and the lifetimes of Italian semi-supercentenarians.