Behavior of the empirical Wasserstein distance in R^d under moment conditions

Jérôme Dedecker; Florence Merlevède

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arXiv · 1807.09031

Behavior of the empirical Wasserstein distance in R^d under moment conditions

Jérôme Dedecker·Florence Merlevède

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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 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. Mathematics subject classification. 60B10, 60F10, 60F15, 60E15.

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Jérôme Dedecker, Florence Merlevède. 2018-07-24. Behavior of the empirical Wasserstein distance in R^d under moment conditions. https://arxiv.org/abs/1807.09031

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