{
  "id": "2207.14402",
  "version": "v1",
  "published": "2022-07-28T22:50:51.000Z",
  "updated": "2022-07-28T22:50:51.000Z",
  "title": "Non-uniform bounds and Edgeworth expansions in self-normalized limit theorems",
  "authors": [
    "Pascal Beckedorf",
    "Angelika Rohde"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We study Edgeworth expansions in limit theorems for self-normalized sums. Non-uniform bounds for expansions in the central limit theorem are established while only imposing minimal moment conditions. Within this result, we address the case of non-integer moments leading to a reduced remainder. Furthermore, we provide non-uniform bounds for expansions in local limit theorems. The enhanced tail-accuracy of our non-uniform bounds allows for deriving an Edgeworth-type expansion in the entropic central limit theorem as well as a central limit theorem in total variation distance for self-normalized sums.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-28T22:50:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05",
      "62E20"
    ],
    "keywords": [
      "non-uniform bounds",
      "self-normalized limit theorems",
      "entropic central limit theorem",
      "self-normalized sums",
      "imposing minimal moment conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}