{
  "id": "1503.00113",
  "version": "v1",
  "published": "2015-02-28T10:56:07.000Z",
  "updated": "2015-02-28T10:56:07.000Z",
  "title": "Behavior of the Wasserstein distance between the empirical and the marginal distributions of stationary $α$-dependent sequences",
  "authors": [
    "Jérôme Dedecker",
    "Florence Merlevède"
  ],
  "categories": [
    "math.PR"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-28T10:56:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "wasserstein distance",
      "marginal distribution",
      "dependent sequences",
      "stationary",
      "central limit theorem holds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}