{
  "id": "1711.05112",
  "version": "v2",
  "published": "2017-11-14T14:34:17.000Z",
  "updated": "2018-10-30T13:22:49.000Z",
  "title": "Weak Convergence of Sequential Empirical Processes under Weak Dependence",
  "authors": [
    "Maria Mohr"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "The purpose of this paper is to prove a weak convergence result for empirical processes indexed in general classes of functions and with an underlying $\\alpha$-mixing sequence of random variables. In particular the uniformly boundedness assumption on the function class, which is required in most of the existing literature, is spared. Furthermore under strict stationarity a weak convergence result for the sequential empirical process indexed in function classes is obtained, as a direct consequence. Two examples in mathematical statistics, that cannot be treated with existing results, are given as possible applications.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2018-10-30T13:22:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05",
      "60F17"
    ],
    "keywords": [
      "sequential empirical process",
      "weak dependence",
      "weak convergence result",
      "function class",
      "general classes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}