Blanchet, J., He, F. & Murthy, K. On distributionally robust extreme value analysis. Extremes 23, 317–347 (2020). https://doi.org/10.1007/s10687-019-00371-1

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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.

Authors
Jose Blanchet, Fei He, Karthyek Murthy
Publication date
2020/6
Journal
Extremes
Volume
23
Pages
317-347
Publisher
Springer US