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A Central Limit Theorem for Wasserstein type distances between two distinct univariate distributions

Abstract : In this article we study the natural nonparametric estimator of a Wasserstein type cost between two distinct continuous distributions F and G on R. The estimator is based on the order statistics of a sample having marginals F, G and any joint distribution. We prove a central limit theorem under general conditions relating the tails and the cost function. In particular, these conditions are satisfied by Wasserstein distances of order p>1and compatible classical probability distributions.
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Contributor : Laurence Porte <>
Submitted on : Tuesday, April 21, 2020 - 10:11:16 AM
Last modification on : Wednesday, April 29, 2020 - 11:24:27 AM

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Philippe Berthet, Jean-Claude Fort, Thierry Klein. A Central Limit Theorem for Wasserstein type distances between two distinct univariate distributions. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, Institute Henri Poincaré, 2020, 56 (2), pp.954-982. ⟨10.1214/19-AIHP990⟩. ⟨hal-02548977⟩

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