Kendall quantile ordering on R 2 , probabilistic transport maps and their empirical counterpart - MAP5 Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2023

Kendall quantile ordering on R 2 , probabilistic transport maps and their empirical counterpart

Résumé

We build a universal r.v. generator from the intrinsic geometry induced by what we define to be the Kendall quantile ordering of probability distribution functions on R 2 , having its own statistical interest. Using this generator we define a closed form transport map τ F G between any smooth distributions F and G. This τ F G is optimal when reduced to the Kendall quantile curves, for a large class of coordinate-wise convex costs. It coincides with the optimal transport if F and G share the same copula. The empirical counterpart τ n,m of τ F G is a non parametric transport plan that is easy to compute even for large samples. We illustrate the probabilistic geometry of τ F G by simulations of τ n,m that exhibit good performance with respect to the L 2 Wasserstein distance, and point out some statistical applications.
Fichier principal
Vignette du fichier
Kendall_Geometry_Berthet_Fort.pdf (1.09 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03987676 , version 1 (14-02-2023)
hal-03987676 , version 2 (06-11-2023)

Identifiants

  • HAL Id : hal-03987676 , version 1

Citer

Philippe Berthet, Jean-Claude Fort. Kendall quantile ordering on R 2 , probabilistic transport maps and their empirical counterpart. 2023. ⟨hal-03987676v1⟩
60 Consultations
65 Téléchargements

Partager

Gmail Facebook X LinkedIn More