Convergence of an estimator of the Wasserstein distance between two continuous probability distributions

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.
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Submitted on : Tuesday, May 23, 2017 - 4:02:40 PM
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Thierry Klein, Jean-Claude Fort, Philippe Berthet. Convergence of an estimator of the Wasserstein distance between two continuous probability distributions. 2017. ⟨hal-01526879⟩

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