{
  "id": "1807.05741",
  "version": "v1",
  "published": "2018-07-16T09:06:49.000Z",
  "updated": "2018-07-16T09:06:49.000Z",
  "title": "Wasserstein-2 bounds in normal approximation under local dependence",
  "authors": [
    "Xiao Fang"
  ],
  "comment": "14 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We obtain a general bound for the Wasserstein-2 distance in normal approximation for sums of locally dependent random variables. The proof is based on an asymptotic expansion for expectations of second-order differentiable functions of the sum. Applied to subgraph counts in the Erd\\H{o}s-R\\'enyi random graph, our result shows that the Wasserstein-1 bound of Barbour, Karo\\'nski and Ruci\\'nski (1989) holds for the stronger Wasserstein-2 distance.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-16T09:06:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "normal approximation",
      "local dependence",
      "locally dependent random variables",
      "general bound",
      "random graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}