Abstract
We establish some deviation inequalities, moment bounds and almost sure results for the Wasserstein distance of order $p\in [1, \infty )$ between the empirical measure of independent and identically distributed ${\mathbb R}^d$-valued random variables and the common distribution of the variables. We only assume the existence of a (strong or weak) moment of order $rp$ for some $r>1$, and we discuss the optimality of the bounds.
Citation
Jérôme Dedecker. Florence Merlevède. "Behavior of the empirical Wasserstein distance in ${\mathbb R}^d$ under moment conditions." Electron. J. Probab. 24 1 - 32, 2019. https://doi.org/10.1214/19-EJP266
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