{
  "id": "1609.03970",
  "version": "v1",
  "published": "2016-09-13T18:34:45.000Z",
  "updated": "2016-09-13T18:34:45.000Z",
  "title": "Multivariate normal approximation of the maximum likelihood estimator via the delta method",
  "authors": [
    "Andreas Anastasiou",
    "Robert E. Gaunt"
  ],
  "comment": "11 pages",
  "categories": [
    "math.ST",
    "stat.TH"
  ],
  "abstract": "We use the delta method and Stein's method to derive, under regularity conditions, explicit upper bounds for the distributional distance between the distribution of the maximum likelihood estimator (MLE) of a $d$-dimensional parameter and its asymptotic multivariate normal distribution. Our bounds apply in situations in which the MLE can be written as a function of a sum of i.i.d. $t$-dimensional random vectors. We apply our general bound to establish a bound for the multivariate normal approximation of the MLE of the normal distribution with unknown mean and variance.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-13T18:34:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05",
      "62E17",
      "62F12"
    ],
    "keywords": [
      "multivariate normal approximation",
      "maximum likelihood estimator",
      "delta method",
      "asymptotic multivariate normal distribution",
      "explicit upper bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}