Behavior of the empirical Wasserstein distance in \({\mathbb R}^d\) under moment conditions
DOI10.1214/19-EJP266zbMath1406.60009arXiv1807.09031OpenAlexW2883361795MaRDI QIDQ1721999
Florence Merlevède, Jérôme Dedecker
Publication date: 14 February 2019
Published in: Electronic Journal of Probability (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1807.09031
moment inequalitiesempirical measureWasserstein distancedeviation inequalitiesindependent and identically distributed random variablesalmost sure rates of convergence
Inequalities; stochastic orderings (60E15) Strong limit theorems (60F15) Large deviations (60F10) Convergence of probability measures (60B10)
Related Items (2)
Cites Work
- Unnamed Item
- Constructive quantization: approximation by empirical measures
- On the rate of convergence in Wasserstein distance of the empirical measure
- Behavior of the Wasserstein distance between the empirical and the marginal distributions of stationary \(\alpha\)-dependent sequences
- On optimal matchings
- Matching random samples in many dimensions
- Asymptotics for transportation cost in high dimensions
- Asymptotics for \(L_2\) functionals of the empirical quantile process, with applications to tests of fit based on weighted Wasserstein distances
- Central limit theorems for the Wasserstein distance between the empirical and the true distributions
- Optimum bounds for the distributions of martingales in Banach spaces
- Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance
- Uniform rates of the Glivenko-Cantelli convergence and their use in approximating Bayesian inferences
- On the mean speed of convergence of empirical and occupation measures in Wasserstein distance
- On the subspaces of \(L^p\) \((p > 2)\) spanned by sequences of independent random variables
- Combinatorial Optimization Over Two Random Point Sets
- Inequalities for Probabilities of Large Deviations in Terms of Pseudo-Moments
- Empirical measures: regularity is a counter-curse to dimensionality
- One-dimensional empirical measures, order statistics, and Kantorovich transport distances
- Inequalities for the $r$th Absolute Moment of a Sum of Random Variables, $1 \leqq r \leqq 2$
- Convergence Rates in the Law of Large Numbers
- The Speed of Mean Glivenko-Cantelli Convergence
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