{
  "id": "1712.03667",
  "version": "v1",
  "published": "2017-12-11T07:51:57.000Z",
  "updated": "2017-12-11T07:51:57.000Z",
  "title": "Berry-Esseen bounds for self-normalized martingales",
  "authors": [
    "Xiequan Fan",
    "Qi-Man Shao"
  ],
  "journal": "Commun. Math. Stat. 2017",
  "categories": [
    "math.PR"
  ],
  "abstract": "A Berry-Esseen bound is obtained for self-normalized martingales under the assumption of finite moments. The bound coincides with the classical Berry-Esseen bound for standardized martingales. An example is given to show the optimality of the bound. Applications to Student's statistic and autoregressive process are also discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-11T07:51:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G42",
      "60F05",
      "60E15"
    ],
    "keywords": [
      "self-normalized martingales",
      "finite moments",
      "bound coincides",
      "classical berry-esseen bound",
      "students statistic"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}