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Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance
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Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance
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Journal Article
Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance
2019
Overview
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 µ approaches µ 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 spaces. Our finite-sample results show the existence of multi-scale behavior, where measures can exhibit radically different rates of convergence as n grows.
Publisher
International Statistical Institute (ISI)
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