Estimation of deformations between distributions by minimal Wasserstein distance.

Hélène Lescornel (1) , Jean-Michel Loubes (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

We consider the issue of estimating a measure observed in a deformation framework. For this we consider a parametric deformation model on an empirical sample and provide a new matching criterion for cloud points based on a generalization of the registration criterion used in a paper of F. Gamboa, J-M Loubes and E. Maza entitled Semi-parametric estimation of shits and published in 2007. We study the asymptotic behaviour of the estimators of the deformations and provide some examples to some particular deformation models.

Mots clés: Distribution registration; Wasserstein distance; M-estimation

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Hélène Lescornel, Jean-Michel Loubes. Estimation of deformations between distributions by minimal Wasserstein distance.. 2012. ⟨hal-00749519v1⟩