On Wasserstein Two-Sample Testing and Related Families of Nonparametric Tests

DOI Web Site 6 Citations
  • Aaditya Ramdas
    Departments of Statistics and Computer Science, University of California, Berkeley, CA 94703, USA
  • Nicolás Trillos
    Department of Mathematics, Brown University, Providence, RI 02912, USA
  • Marco Cuturi
    Laboratory of Statistics, CREST, ENSAE, Université Paris-Saclay, Malakoff 92240, France

Description

<jats:p>Nonparametric two-sample or homogeneity testing is a decision theoretic problem that involves identifying differences between two random variables without making parametric assumptions about their underlying distributions. The literature is old and rich, with a wide variety of statistics having being designed and analyzed, both for the unidimensional and the multivariate setting. In this short survey, we focus on test statistics that involve the Wasserstein distance. Using an entropic smoothing of the Wasserstein distance, we connect these to very different tests including multivariate methods involving energy statistics and kernel based maximum mean discrepancy and univariate methods like the Kolmogorov–Smirnov test, probability or quantile (PP/QQ) plots and receiver operating characteristic or ordinal dominance (ROC/ODC) curves. Some observations are implicit in the literature, while others seem to have not been noticed thus far. Given nonparametric two-sample testing’s classical and continued importance, we aim to provide useful connections for theorists and practitioners familiar with one subset of methods but not others.</jats:p>

Journal

  • Entropy

    Entropy 19 (2), 47-, 2017-01-26

    MDPI AG

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