{
  "id": "2005.05208",
  "version": "v1",
  "published": "2020-05-11T15:53:11.000Z",
  "updated": "2020-05-11T15:53:11.000Z",
  "title": "Wasserstein distance error bounds for the multivariate normal approximation of the maximum likelihood estimator",
  "authors": [
    "Andreas Anastasiou",
    "Robert E. Gaunt"
  ],
  "comment": "31 pages, 1 figure",
  "categories": [
    "math.ST",
    "stat.TH"
  ],
  "abstract": "We obtain explicit Wasserstein distance error bounds between the distribution of the multi-parameter MLE and the multivariate normal distribution. Our general bounds are given for possibly high-dimensional, independent and identically distributed random vectors. Our general bounds are of the optimal $\\mathcal{O}(n^{-1/2})$ order. We apply our general bounds to derive Wasserstein distance error bounds for the multivariate normal approximation of the MLE in several settings; these being single-parameter exponential families, the normal distribution under canonical parametrisation, and the multivariate normal distribution under non-canonical parametrisation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-11T15:53:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05",
      "62E17",
      "62F10",
      "62F12"
    ],
    "keywords": [
      "multivariate normal approximation",
      "maximum likelihood estimator",
      "multivariate normal distribution",
      "general bounds",
      "explicit wasserstein distance error bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}