On the rate of convergence of empirical measure in ∞-Wasserstein distance for unbounded density function

07/22/2018

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by   Anning Liu, et al.

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Duke University

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Tsinghua University

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We consider a sequence of identically independently distributed random samples from an absolutely continuous probability measure in one dimension with unbounded density. We establish a new rate of convergence of the ∞-Wasserstein distance between the empirical measure of the samples and the true distribution, which extends the previous convergence result by Trilllos and Slepčev to the case of unbounded density.