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

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

1 Universidad Valladolid
2 IMT - Institut de Mathématiques de Toulouse UMR5219

Wasserstein barycenters and variance-like criterion using Wasser-stein 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 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.

Domaines: Statistiques [math.ST]

Eustasio del Barrio, Hélène Lescornel, Jean-Michel Loubes. Central Limit Theorem and bootstrap procedure for Wasserstein's barycenter variations and application to structural relationships between distributions. 2016. ⟨hal-01269785v1⟩