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

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

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

We propose a study of a distribution registration model for general deformation functions. In this framework, we provide estimators of the deformations as well as a goodness of fit test of the model. For this, we consider a criterion which studies the Fréchet mean (or barycenter) of the warped distributions whose study enables to make inference on the model. In particular we obtain the asymptotic distribution and a bootstrap procedure for the Wasserstein variation.

Mots clés: Central Limit Theorem; Goodness-of-fit; Wasserstein distance

Domaines: Statistiques [math.ST]; Machine Learning [stat.ML]

Eustasio del Barrio, Paula Gordaliza, Hélène Lescornel, Jean-Michel Loubes. Central limit theorem and bootstrap procedure for Wasserstein’s variations with an application to structural relationships between distributions. 2018. ⟨hal-01187232v3⟩