Jose Blanchet, Karthyek Murthy, Nian Si, Confidence regions in Wasserstein distributionally robust estimation, Biometrika, Volume 109, Issue 2, June 2022, Pages 295–315, https://doi.org/10.1093/biomet/asab026
Abstract
Estimators based on Wasserstein distributionally robust optimization are obtained as solutions of min-max problems in which the statistician selects a parameter minimizing the worst-case loss among all probability models within a certain distance from the underlying empirical measure in a Wasserstein sense. While motivated by the need to identify optimal model parameters or decision choices that are robust to model misspecification, these distributionally robust estimators recover a wide range of regularized estimators, including square-root lasso and support vector machines, among others. This paper studies the asymptotic normality of these distributionally robust estimators as well as the properties of an optimal confidence region induced by the Wasserstein distributionally robust optimization formulation. In addition, key properties of min-max distributionally robust optimization problems are also studied …
Authors: Jose Blanchet, Karthyek Murthy, Nian Si
Publication date: 2022/6/1
Journal: Biometrika
Volume: 109
Issue: 2
Pages: 295-315
Publisher: Oxford University Press
