• Bernoulli
  • Volume 23, Number 3 (2017), 2083-2127.

Behavior of the Wasserstein distance between the empirical and the marginal distributions of stationary $\alpha$-dependent sequences

Jérôme Dedecker and Florence Merlevède

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We study the Wasserstein distance of order 1 between the empirical distribution and the marginal distribution of stationary $\alpha$-dependent sequences. We prove some moments inequalities of order $p$ for any $p\geq1$, 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, Volume 23, Number 3 (2017), 2083-2127.

Received: February 2015
Revised: October 2015
First available in Project Euclid: 17 March 2017

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central limit theorem empirical process intermittency moments inequalities stationary sequences Wasserstein distance


Dedecker, Jérôme; Merlevède, Florence. Behavior of the Wasserstein distance between the empirical and the marginal distributions of stationary $\alpha$-dependent sequences. Bernoulli 23 (2017), no. 3, 2083--2127. doi:10.3150/16-BEJ805.

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