IDEAS home Printed from
   My bibliography  Save this paper

Multivariate Goodness-of-Fit Tests Based on Wasserstein Distance


  • Marc Hallin
  • Gilles Mordant
  • Johan Segers


Goodness-of-fit tests based on the empirical Wasserstein distance are proposed for simple and composite null hypotheses involving general multivariate distributions. This includes the important problem of testing for multivariate normality with unspecified location and covariance and, more generally, testing for elliptical symmetry with given standard radial density, unspecified location and scatter parameters. The calculation of test statistics boils down to solving the well-studied semi-discrete optimal transport problem. Exact critical values can be computed for some important particular cases, such as null hypotheses of ellipticity with given standard radial density and unspecified location and scatter; else, approximate critical values are obtained via parametric bootstrap. Consistency is established, based on a result on the convergence to zero, uniformly over certain families of distributions, of the empirical Wasserstein distance---a novel result of independent interest. A simulation study establishes the practical feasibility and excellent performance of the proposed tests.

Suggested Citation

  • Marc Hallin & Gilles Mordant & Johan Segers, 2020. "Multivariate Goodness-of-Fit Tests Based on Wasserstein Distance," Working Papers ECARES 2020-06, ULB -- Universite Libre de Bruxelles.
  • Handle: RePEc:eca:wpaper:2013/303372

    Download full text from publisher

    File URL:
    File Function: Full text for the whole work, or for a work part
    Download Restriction: no

    Other versions of this item:


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Solveig Flaig & Gero Junike, 2022. "Scenario Generation for Market Risk Models Using Generative Neural Networks," Risks, MDPI, vol. 10(11), pages 1-28, October.
    2. Marc Hallin & H Lui & Thomas Verdebout, 2022. "Nonparametric Measure-transportation-based Methods for Directional Data," Working Papers ECARES 2022-18, ULB -- Universite Libre de Bruxelles.
    3. Hongjian Shi & Marc Hallin & Mathias Drton & Fang Han, 2020. "Rate-Optimality of Consistent Distribution-Free Tests of Independence Based on Center-Outward Ranks and Signs," Working Papers ECARES 2020-23, ULB -- Universite Libre de Bruxelles.
    4. Chen, Feifei & Jiménez–Gamero, M. Dolores & Meintanis, Simos & Zhu, Lixing, 2022. "A general Monte Carlo method for multivariate goodness–of–fit testing applied to elliptical families," Computational Statistics & Data Analysis, Elsevier, vol. 175(C).
    5. Solveig Flaig & Gero Junike, 2021. "Scenario generation for market risk models using generative neural networks," Papers 2109.10072,, revised Aug 2023.


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eca:wpaper:2013/303372. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Benoit Pauwels (email available below). General contact details of provider: .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.