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 deformation operator acting on measures. For this we consider a parametric warping model on an empirical sample and provide a new matching criterion for cloud points based on a generalization of the registration criterion used in [Gamboa-Loubes-Maza 2007]. We study the asymptotic behaviour of the estimator of the deformation 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. 2014. ⟨hal-00749519v2⟩