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

Jérôme Dedecker; Florence Merlevède

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arXiv · 1503.00113

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

Jérôme Dedecker·Florence Merlevède

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Abstract

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 $\ge$ 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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BibTeX RIS

Jérôme Dedecker, Florence Merlevède. 2015-02-28. Behavior of the Wasserstein distance between the empirical and the marginal distributions of stationary $\alpha$-dependent sequences. https://arxiv.org/abs/1503.00113

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