Central limit theorem and bootstrap procedure for Wasserstein's   variations with an application to structural relationships between   distributions
  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. 
Eustasio Del Barrio, Paula Gordaliza, H\'el\`ene Lescornel (IMT),   Jean-Michel Loubes (IMT)
math.ST stat.TH