A Central Limit Theorem for Wasserstein type distances between two different laws

Philippe Berthet (1) , Jean-Claude Fort (2) , Thierry Klein (3)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
3 ENAC - Ecole Nationale de l'Aviation Civile

This article is dedicated to the estimation of Wasserstein distances and Wasserstein costs between two distinct continuous distributions $F$ and $G$ on $\mathbb R$. The estimator is based on the order statistics of (possibly dependent) samples of $F$ resp. $G$. We prove the consistency and the asymptotic normality of our estimators. \\

Mots clés: Central Limit Theorems; Generelized Wasserstein distances; Dependent samples.; Empirical processes; Strong approximation

Domaines: Probabilités [math.PR]; Statistiques [math.ST]

Philippe Berthet, Jean-Claude Fort, Thierry Klein. A Central Limit Theorem for Wasserstein type distances between two different laws. 2017. ⟨hal-01624786v1⟩