Central limit theorem and bootstrap procedure for Wasserstein’s variations with an application to structural relationships between distributions

Eustasio del Barrio, Paula Gordaliza, Hélène Lescornel and Jean-Michel Loubes

Journal of Multivariate Analysis, 2019, vol. 169, issue C, 341-362

Abstract: Wasserstein barycenters and variance-like criteria based on the Wasserstein distance are used in many problems to analyze the homogeneity of collections of distributions and structural relationships between the observations. We propose the estimation of the quantiles of the empirical process of Wasserstein’s variation using a bootstrap procedure. We then use these results for statistical inference on a distribution registration model for general deformation functions. The tests are based on the variance of the distributions with respect to their Wasserstein’s barycenters for which we prove central limit theorems, including bootstrap versions.

Keywords: Central limit theorem; Goodness-of-fit; Wasserstein distance (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.jmva.2018.09.014

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