Central limit theorems for the wasserstein distance between the empirical and the true distributions

By Eustasio del Barrio, Evarist Gin'e, Carlos Matrán. 1999

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Citations in the corpus

Personalized Federated Learning: A Meta-Learning Approach (2020, neutral): “In this case, we have W1(pi, pu) = O(1/ √ m) [42].”
Statistical Aspects of Wasserstein Distances (2018, background): “For example, in order to test the ﬁt to some normal distribution, del Barrio et al. (1999a) ﬁnd the asymptotic distribution of the test statistic an inﬁnite sum of rescaled and centred χ 2 random variables (under the null hypothesis).”
Asymptotics for L2 functionals of the empirical quantile process, with applications to tests of fit based on weighted Wasserstein distances (2005, methodology): “The second object is to apply the results obtained to testing the fit of empirical data to location–scale families of distributions by means of weighted Wasserstein distances, as suggested by the work of del Barrio et al. (1999a; 2000), de Wet (2000; 2002) and Csörgő (2002).”
Decentralize and Randomize: Faster Algorithm for Wasserstein Barycenters (2018, methodology): “If the objects in the set are randomly sampled from some distribution, theoretical results such as central limit theorem [14] or confidence set construction [20] have been proposed, providing the basis for the practical use of Wasserstein barycenter.”
On the mean speed of convergence of empirical and occupation measures in Wasserstein distance (2011, unknown): “Matrán [8] obtain a central limit theorem for W1(Ln,μ) under the condition that ∫ +∞ −∞ √ F(t)(1 − F(t))dt < +∞ where F is the cumulative distribution function (c.”
Simple Bounds for the Convergence of Empirical and Occupation Measures in 1-Wasserstein Distance (2011, background): “The behaviour of the Wasserstein distance between empirical and true distribution in one dimension has been very thoroughly studied by del Barrio, Giné, Matran, see [9].”
Personalized Federated Learning with Theoretical Guarantees: A Model-Agnostic Meta-Learning Approach (2020, unknown): “In this case, we have W1(pi, pu) = O(1/ √ m) [41].”