{
  "id": "2112.05815",
  "version": "v1",
  "published": "2021-12-10T20:15:32.000Z",
  "updated": "2021-12-10T20:15:32.000Z",
  "title": "A multivariate CLT for <<typical>> weighted sums with rate of convergence of order O(1/n)",
  "authors": [
    "Sagak A. Ayvazyan",
    "Vladimir V. Ulyanov"
  ],
  "comment": "29 pages",
  "doi": "10.1007/978-3-031-30114-8_6",
  "categories": [
    "math.PR"
  ],
  "abstract": "The \"typical\" asymptotic behavior of the weighted sums of independent random vectors in $k$-dimensional space is considered. It is shown that in this case the rate of convergence in the multivariate central limit theorem is of order $O(1/n)$. This extends the one-dimensional Klartag and Sodin (2011) result.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-12-10T20:15:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05"
    ],
    "keywords": [
      "weighted sums",
      "multivariate clt",
      "convergence",
      "multivariate central limit theorem",
      "independent random vectors"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}