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 x−y 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.
Domaines
Probabilités [math.PR]Origine | Fichiers produits par l'(les) auteur(s) |
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