A Distributionally Robust Optimization Framework for Extreme Event Estimation

Journal of the American Statistical Association · Tue

DOI: 10.1080/01621459.2026.2731641

Abstract

Conventional methods for extreme event estimation rely on well-chosen parametric models asymptotically justified from extreme value theory (EVT). These methods, while powerful and theoretically grounded, could however encounter a bias-variance tradeoff that becomes more difficult to tackle when the data size is too small, deteriorating the reliability of the tail estimation. In this paper, we study a framework based on the recently surging literature of distributionally robust optimization. This approach can be viewed as a nonparametric alternative to conventional EVT, by imposing general shape belief on the tail instead of parametric assumption and using worst-case optimization as a resolution to handle the nonparametric uncertainty. We explain how this approach bypasses the bias-variance tradeoff in EVT. On the other hand, we face a conservativeness-variance tradeoff which we describe how to tackle. We also demonstrate computational tools for the involved optimization problems and compare our performance with conventional EVT across a range of numerical examples.

Keywords

distributionally robust optimization, extreme event analysis, confidence bounds, shape constraint, semi-definite programming

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