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Article Dans Une Revue Electronic Journal of Probability Année : 2019

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

Résumé

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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Dates et versions

hal-01847304 , version 1 (23-07-2018)
hal-01847304 , version 2 (19-12-2018)

Identifiants

Citer

Jérôme Dedecker, Florence Merlevède. Behavior of the empirical Wasserstein distance in R^d under moment conditions. Electronic Journal of Probability, 2019, 24 (none), ⟨10.1214/19-EJP266⟩. ⟨hal-01847304v2⟩
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