# On distributionally robust extreme value analysis

arXiv: https://arxiv.org/abs/1601.06858 · HTML: https://mlsanity.com/paper/1601.06858/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jan 2016.

## Built on by (most cited first, 2 of 2)

- [Evaluating Model Performance Under Worst-case Subpopulations](https://mlsanity.com/paper/2407.01316/) (2024)
- [Quantum enhanced rare event discovery and sampling](https://mlsanity.com/paper/2606.06316/) (2026)

## Abstract (arXiv)

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.