On distributionally robust extreme value analysis

TL;DR

This paper introduces a data-driven, distributionally robust approach to extreme value analysis that accounts for model uncertainty and improves the estimation of extreme quantiles beyond standard EVT methods.

Contribution

It extends distributional robustness in EVT by exploring various discrepancy measures and provides rigorous results and practical illustrations for better extreme quantile estimation.

Findings

Standard EVT can underestimate extreme quantiles

The proposed method improves robustness against model misspecification

Different discrepancy measures influence the robustness of estimates

Abstract

We study distributional robustness in the context of Extreme Value Theory (EVT). We provide a data-driven method for estimating extreme quantiles in a manner that is robust against incorrect model assumptions underlying the application of the standard Extremal Types Theorem. Typical studies in distributional robustness involve computing worst case estimates over a model uncertainty region expressed in terms of the Kullback-Leibler discrepancy. We go beyond standard distributional robustness in that we investigate different forms of discrepancies, and prove rigorous results which are helpful for understanding the role of a putative model uncertainty region in the context of extreme quantile estimation. Finally, we illustrate our data-driven method in various settings, including examples showing how standard EVT can significantly underestimate quantiles of interest.