A Central Limit Theorem for Wasserstein type distances between two different laws
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This article is dedicated to the estimation of Wasserstein distances and Wasserstein costs between two distinct continuous distributions F and G on 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: Central Limit Theorems- Generelized Wasserstein distances- Empirical processes- Strong approximation- Dependent samples.
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