Behavior of the Wasserstein distance between the empirical and the marginal distributions of stationary α-dependent sequences

Abstract : We study the Wasserstein distance of order 1 between the empirical distribution and the marginal distribution of stationary α-dependent sequences. We prove some moments inequalities of order p for any p ≥ 1, and we give some conditions under which the central limit theorem holds. We apply our results to unbounded functions of expanding maps of the interval with a neutral fixed point at zero. The moment inequalities for the Wasserstein distance are similar to the well known von Bahr-Esseen or Rosenthal bounds for partial sums, and seem to be new even in the case of independent and identically distributed random variables.
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Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2017, pp.2083-2127
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https://hal.archives-ouvertes.fr/hal-01121156
Contributeur : Jérôme Dedecker <>
Soumis le : vendredi 27 février 2015 - 15:35:01
Dernière modification le : lundi 20 mars 2017 - 11:40:51
Document(s) archivé(s) le : vendredi 29 mai 2015 - 11:10:45

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  • HAL Id : hal-01121156, version 1
  • ARXIV : 1503.00113

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Jérôme Dedecker, Florence Merlevède. Behavior of the Wasserstein distance between the empirical and the marginal distributions of stationary α-dependent sequences. Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2017, pp.2083-2127. <hal-01121156>

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