On the rate of convergence of empirical measures in $\infty$-transportation distance

Abstract

We consider random i.i.d. samples of absolutely continuous measures on bounded connected domains. We prove an upper bound on the $\infty$-transportation distance between the measure and the empirical measure of the sample. The bound is optimal in terms of scaling with the number of sample points.

References in corpus (1)

• Partial regularity and smooth topology-preserving approximations of rough domains

Cited by in corpus (1)

• Robust estimation of superhedging prices