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


Journal Article

© 2019 Brown University. 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.

Full Text

Duke Authors

Cited Authors

  • Liu, A; Liu, JG; Lu, Y

Published Date

  • January 1, 2019

Published In

Volume / Issue

  • 77 / 4

Start / End Page

  • 811 - 829

Electronic International Standard Serial Number (EISSN)

  • 1552-4485

International Standard Serial Number (ISSN)

  • 0033-569X

Digital Object Identifier (DOI)

  • 10.1090/qam/1541

Citation Source

  • Scopus