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arXiv · 1807.08365

On the rate of convergence of empirical measure in $\infty-$Wasserstein distance for unbounded density function

Anning Liu·Jian-Guo Liu·Yulong Lu
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Abstract

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 $\infty-$Wasserstein distance between the empirical measure of the samples and the true distribution, which extends the previous convergence result by Trilllos and Slep\v{c}ev to the case that the true distribution has an unbounded density.

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Anning Liu, Jian-Guo Liu, Yulong Lu. 2018-07-22. On the rate of convergence of empirical measure in $\infty-$Wasserstein distance for unbounded density function. https://arxiv.org/abs/1807.08365

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