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

Abstract

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. \begin{it}Keywords:\end{it} Central Limit Theorems- Generelized Wasserstein distances- Empirical processes- Strong approximation- Dependent samples.

References in corpus (1)

• Revisiting two strong approximation results of Dudley and Philipp

Cited by in corpus (2)

• Central Limit Theorems for General Transportation Costs
• Gromov-Wasserstein Distance based Object Matching: Asymptotic Inference