A statistical analysis of a deformation model with Wasserstein barycenters : estimation procedure and goodness of fit test

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

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.

Domaines: Statistiques [math.ST]

Eustasio del Barrio, Hélène Lescornel, Jean-Michel Loubes. A statistical analysis of a deformation model with Wasserstein barycenters : estimation procedure and goodness of fit test. 2015. ⟨hal-01187232v1⟩