Sample Out-of-Sample Inference Based on Wasserstein Distance

Jose Blanchet () and Yang Kang ()
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Jose Blanchet: Department of Management Science and Engineering, Stanford University, Stanford, California 94305
Yang Kang: Department of Statistics, Columbia University, New York, New York 10027

Operations Research, 2021, vol. 69, issue 3, 985-1013

Abstract: We present a novel inference approach that we call sample out-of-sample inference. The approach can be used widely, ranging from semisupervised learning to stress testing, and it is fundamental in the application of data-driven distributionally robust optimization. Our method enables measuring the impact of plausible out-of-sample scenarios in a given performance measure of interest, such as a financial loss. The methodology is inspired by empirical likelihood (EL), but we optimize the empirical Wasserstein distance (instead of the empirical likelihood) induced by observations. From a methodological standpoint, our analysis of the asymptotic behavior of the induced Wasserstein-distance profile function shows dramatic qualitative differences relative to EL. For instance, in contrast to EL, which typically yields chi-squared weak convergence limits, our asymptotic distributions are often not chi-squared. Also, the rates of convergence that we obtain have some dependence on the dimension in a nontrivial way but remain controlled as the dimension increases.

Keywords: decision analysis: inference; probability: stochastic model applications; financial institutions: banks, Stochastic Models, nonparametric statistics, probability, distributionally robust optimization, optimal transport, Wasserstein distance (search for similar items in EconPapers)
Date: 2021
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