On the rate of convergence of empirical measures in $\infty$-transportation distance
By Nicolás García Trillos, Dejan Slepvcev. 2014
53 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/0916f32ab9dd0c9c147a7d281b089971416cc49e
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In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- Regret in the Newsvendor Model with Demand and Yield Randomness (2021, methodology): “…and yield has a compact support and a probability density/ mass function bounded from below by a positive constant almost everywhere, theorem 1.1 in Trillos and Slepˇcev (2015) suggests that it suffices to set the Wasserstein radius θ in an order of N − 1/2 log ( N ) 3/4 with respect to the sample…”