# Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance

@article{Weed2017SharpAA, title={Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance}, author={Jonathan Weed and Francis R. Bach}, journal={Bernoulli}, year={2017} }

The Wasserstein distance between two probability measures on a metric space is a measure of closeness with applications in statistics, probability, and machine learning. In this work, we consider the fundamental question of how quickly the empirical measure obtained from $n$ independent samples from $\mu$ approaches $\mu$ in the Wasserstein distance of any order. We prove sharp asymptotic and finite-sample results for this rate of convergence for general measures on general compact metric…

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