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

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

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: Dependent samples.; Central Limit Theorems-Generelized Wasserstein distances-Empirical; Strong approximation; Empirical processes; Generelized Wasserstein distances; MSC Classification:; processes-Strong approximation-Dependent samples; Central Limit Theorems; 62G30; 62G20; 60F05; 60F17

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. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2020, ⟨10.1214/19-AIHP990⟩. ⟨hal-01624786v2⟩