Optimal-Transport Based Multivariate Goodness-of-Fit Tests

Fuente: arXiv
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Main Authors: Hlávka, Zdeněk, Hudecová, Šárka, Meintanis, Simos G.
Format: Preprint
Published: 2025
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author Hlávka, Zdeněk
Hudecová, Šárka
Meintanis, Simos G.
author_facet Hlávka, Zdeněk
Hudecová, Šárka
Meintanis, Simos G.
contents Characteristic-function based goodness-of-fit tests are suggested for multivariate observations. The test statistics, which are straightforward to compute, are defined as two-sample criteria measuring discrepancy between multivariate ranks of the original observations and the corresponding ranks obtained from an artificial sample generated from the reference distribution under test. Multivariate ranks are constructed using the theory of the optimal measure transport, thus rendering the tests of a simple null hypothesis distribution-free, while bootstrap approximations are still necessary for testing composite null hypotheses. Asymptotic theory is developed and a simulation study, concentrating on comparisons with previously proposed tests of multivariate normality, demonstrates that the method performs well in finite samples.
format Preprint
id arxiv_https___arxiv_org_abs_2507_23490
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Optimal-Transport Based Multivariate Goodness-of-Fit Tests
Hlávka, Zdeněk
Hudecová, Šárka
Meintanis, Simos G.
Statistics Theory
Characteristic-function based goodness-of-fit tests are suggested for multivariate observations. The test statistics, which are straightforward to compute, are defined as two-sample criteria measuring discrepancy between multivariate ranks of the original observations and the corresponding ranks obtained from an artificial sample generated from the reference distribution under test. Multivariate ranks are constructed using the theory of the optimal measure transport, thus rendering the tests of a simple null hypothesis distribution-free, while bootstrap approximations are still necessary for testing composite null hypotheses. Asymptotic theory is developed and a simulation study, concentrating on comparisons with previously proposed tests of multivariate normality, demonstrates that the method performs well in finite samples.
title Optimal-Transport Based Multivariate Goodness-of-Fit Tests
topic Statistics Theory
url https://arxiv.org/abs/2507.23490