Sample Out-of-Sample Inference Based on Wasserstein Distance

被引:4
作者
Blanchet, Jose [1 ]
Kang, Yang [2 ]
机构
[1] Stanford Univ, Dept Management Sci & Engn, Stanford, CA 94305 USA
[2] Columbia Univ, Dept Stat, New York, NY 10027 USA
关键词
nonparametric statistics; probability; distributionally robust optimization; optimal transport; Wasserstein distance; EMPIRICAL LIKELIHOOD; CONFIDENCE-INTERVALS; ESTIMATING EQUATIONS; RATIO; OPTIMIZATION; BANDS;
D O I
10.1287/opre.2020.2028
中图分类号
C93 [管理学];
学科分类号
12 ; 1201 ; 1202 ; 120202 ;
摘要
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.
引用
收藏
页码:985 / 1013
页数:29
相关论文
共 56 条
  • [1] [Anonymous], 2003, STOCHASTIC PROGRAMMI
  • [2] [Anonymous], 2014, Lectures on stochastic programming: modeling and theory
  • [3] [Anonymous], 1973, Introduction to Linear and Nonlinear Programming
  • [4] [Anonymous], 2016, STAT ROBUST OPTIMIZA
  • [5] On the efficient use of the informational content of estimating equations: Implied probabilities and Euclidean empirical likelihood
    Antoine, Bertille
    Bonnal, Helene
    Renault, Eric
    [J]. JOURNAL OF ECONOMETRICS, 2007, 138 (02) : 461 - 487
  • [6] Bayraksan G, 2015, OPERATIONS RES REVOL, P1, DOI DOI 10.1287/EDUC.2015.0134
  • [7] Pathwise versions of the Burkholder-Davis-Gundy inequality
    Beiglboeck, Mathias
    Siorpaes, Pietro
    [J]. BERNOULLI, 2015, 21 (01) : 360 - 373
  • [8] Robust Solutions of Optimization Problems Affected by Uncertain Probabilities
    Ben-Tal, Aharon
    den Hertog, Dick
    De Waegenaere, Anja
    Melenberg, Bertrand
    Rennen, Gijs
    [J]. MANAGEMENT SCIENCE, 2013, 59 (02) : 341 - 357
  • [9] Blake C. L., 1998, UCI REPOSITORY MACHI
  • [10] Blanchet J., 2020, Data Analysis and Applications 3: Computational, Classification, Financial, Statistical and Stochastic Methods