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

Abstract : We establish some deviation inequalities, moment bounds and almost sure results for the Wasserstein distance of order p ∈ [1, ∞) 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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Contributor : Jérôme Dedecker <>
Submitted on : Wednesday, December 19, 2018 - 5:44:42 PM
Last modification on : Thursday, April 11, 2019 - 4:02:54 PM

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  • HAL Id : hal-01847304, version 2
  • ARXIV : 1807.09031

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Jérôme Dedecker, Florence Merlevède. Behavior of the empirical Wasserstein distance in R^d under moment conditions. 2018. ⟨hal-01847304v2⟩

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