A remark on the optimal transport between two probability measures sharing the same copula - Inria - Institut national de recherche en sciences et technologies du numérique
Article Dans Une Revue Statistics and Probability Letters Année : 2014

A remark on the optimal transport between two probability measures sharing the same copula

Résumé

We are interested in the Wasserstein distance between two probability measures on \Rn sharing the same copula C. The image of the probability measure dC by the vectors of pseudo-inverses of marginal distributions is a natural generalization of the coupling known to be optimal in dimension n=1. It turns out that for cost functions c(x,y) equal to the p-th power of the Lq norm of xy in \Rn, this coupling is optimal only when p=q i.e. when c(x,y) may be decomposed as the sum of coordinate-wise costs.
Fichier principal
Vignette du fichier
couploptim.pdf (106.79 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00844906 , version 1 (16-07-2013)

Identifiants

Citer

Aurélien Alfonsi, Benjamin Jourdain. A remark on the optimal transport between two probability measures sharing the same copula. Statistics and Probability Letters, 2014, dx.doi.org/10.1016/j.spl.2013.09.035. ⟨hal-00844906⟩

Altmetric

Partager

More