Multivariate Goodness-of-Fit Tests Based on Wasserstein Distance

Hallin, Marc [UCL] Mordant, Gilles [UCL] Segers, Johan [UCL]

Goodness-of-fit tests based on the empirical Wasserstein dis- tance are proposed for simple and composite null hypotheses involving general multivariate distributions. This includes the important problem of testing for multivariate normality with unspecified mean vector and covari- ance matrix and, more generally, testing for elliptical symmetry with given standard radial density and 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 estab- lishes the practical feasibility and excellent performance of the proposed tests.

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Document type	Document de travail (Working Paper)
Access type	Accès libre
Publication date	2021
Language	Anglais
Number of pages	46 pages
Collection	LIDAM Discussion Paper ISBA - 2021/07
Affiliation	UCL - SSH/LIDAM/ISBA - Institut de Statistique, Biostatistique et Sciences Actuarielles
Links	http://hdl.handle.net/2078.1/245554[Handle]

See also
	[boreal:229090]	Multivariate Goodness-of-Fit Tests Based on Wasserstein Distance
	[boreal:243715]	Multivariate Goodness-of-Fit Tests Based on Wasserstein Distance