# 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. \\
Keywords :
Document type :
Preprints, Working Papers, ...
Domain :

Cited literature [17 references]

https://hal.archives-ouvertes.fr/hal-01624786
Contributor : Thierry Klein <>
Submitted on : Wednesday, November 29, 2017 - 10:09:36 AM
Last modification on : Tuesday, February 11, 2020 - 1:58:03 PM

### Files

Wasserstein_HALrev1.pdf
Files produced by the author(s)

### Identifiers

• HAL Id : hal-01624786, version 2

### Citation

Philippe Berthet, Jean-Claude Fort, Thierry Klein. A Central Limit Theorem for Wasserstein type distances between two different laws. 2017. ⟨hal-01624786v2⟩

Record views