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arXiv · 1710.09763

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

Philippe Berthet·Jean-Claude Fort·Thierry Klein
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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.

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Philippe Berthet, Jean-Claude Fort, Thierry Klein. 2017-10-26. A Central Limit Theorem for Wasserstein type distances between two different laws. https://arxiv.org/abs/1710.09763

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