Central Limit Theorem and bootstrap procedure for Wasserstein's variations with application to structural relationships between distributions

Eustasio del Barrio (1) , Hélène Lescornel (2) , Jean-Michel Loubes (2)

1 UVa - Universidad de Valladolid [Valladolid]
2 IMT - Institut de Mathématiques de Toulouse UMR5219

Wasserstein barycenters and variance-like criterion using Wasserstein distance are used in many problems to analyze the homo-geneity of collections of distributions and structural relationships between the observations. We propose the estimation of the quantiles of the empirical process of the Wasserstein's variation using a bootstrap procedure. Then we 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 a central limit theorem.

Mots clés: Wasserstein distance; Central Limit Theorem for Wasser-stein's variation; goodness of fit

Domaines: Statistiques [math.ST]

Eustasio del Barrio, Hélène Lescornel, Jean-Michel Loubes. Central Limit Theorem and bootstrap procedure for Wasserstein's variations with application to structural relationships between distributions. 2016. ⟨hal-01269785v2⟩