On distributionally robust extreme value analysis

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.

References in corpus (2)

• Likelihood Robust Optimization for Data-driven Problems
• Asymptotic behavior of the generalized St. Petersburg sum conditioned on its maximum

Cited by in corpus (6)

• A precise bare simulation approach to the minimization of some distances. Foundations
• Optimization-based Quantification of Simulation Input Uncertainty via Empirical Likelihood
• On Optimization over Tail Distributions
• Higher-Order Expansion and Bartlett Correctability of Distributionally Robust Optimization
• Distributionally Constrained Black-Box Stochastic Gradient Estimation and Optimization
• Orthounimodal Distributionally Robust Optimization: Representation, Computation and Multivariate Extreme Event Applications