{
  "id": "0706.0844",
  "version": "v1",
  "published": "2007-06-06T19:30:26.000Z",
  "updated": "2007-06-06T19:30:26.000Z",
  "title": "Two multivariate central limit theorems",
  "authors": [
    "Elizabeth Meckes"
  ],
  "comment": "10 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, explicit error bounds are derived in the approximation of rank $k$ projections of certain $n$-dimensional random vectors by standard $k$-dimensional Gaussian random vectors. The bounds are given in terms of $k$, $n$, and a basis of the $k$-dimensional space onto which we project. The random vectors considered are two generalizations of the case of a vector with independent, identically distributed components. In the first case, the random vector has components which are independent but need not have the same distribution. The second case deals with finite exchangeable sequences of random variables.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-06-06T19:30:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "multivariate central limit theorems",
      "dimensional gaussian random vectors",
      "explicit error bounds",
      "dimensional random vectors",
      "second case deals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0706.0844M"
    }
  }
}