{
  "id": "1510.08226",
  "version": "v1",
  "published": "2015-10-28T08:56:46.000Z",
  "updated": "2015-10-28T08:56:46.000Z",
  "title": "Asymptotic expansion of the risk of maximum likelihood estimator with respect to $α$-divergence as a measure of the difficulty of specifying a parametric model --with detailed proof",
  "authors": [
    "Yo Sheena"
  ],
  "comment": "84 pages, 4 figures",
  "categories": [
    "math.ST",
    "stat.TH"
  ],
  "abstract": "For a given parametric probability model, we consider the risk of the maximum likelihood estimator with respect to $\\alpha$-divergence, which includes the special cases of Kullback--Leibler divergence, the Hellinger distance and $\\chi^2$ divergence. The asymptotic expansion of the risk is given with respect to sample sizes of up to order $n^{-2}$. Each term in the expansion is expressed with the geometrical properties of the Riemannian manifold formed by the parametric probability model. We attempt to measure the difficulty of specifying a model through this expansion.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-28T08:56:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F99",
      "62F12"
    ],
    "keywords": [
      "maximum likelihood estimator",
      "asymptotic expansion",
      "parametric model",
      "detailed proof",
      "divergence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 84,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}