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

Anning Liu, Jian Guo Liu, Yulong Lu

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

We consider a sequence of identical 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 Trillos and Slepčev to the case that the true distribution has an unbounded density.

Original languageEnglish (US)
Pages (from-to)811-829
Number of pages19
JournalQuarterly of Applied Mathematics
Volume77
Issue number4
DOIs
StatePublished - 2019
Externally publishedYes

Bibliographical note

Funding Information:
Received August 1, 2018, and, in revised form, March 30, 2019. 2010 Mathematics Subject Classification. Primary 60B10, 68R10. The research was partially supported by KI-Net NSF RNMS11-07444 and NSF DMS-1812573. Email address: lan15@mails.tsinghua.edu.cn Email address: jliu@phy.duke.edu Email address: yulonglu@math.duke.edu

Publisher Copyright:
© 2019 Brown University.

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