{
  "id": "1308.2927",
  "version": "v3",
  "published": "2013-08-13T17:51:00.000Z",
  "updated": "2016-03-30T10:56:48.000Z",
  "title": "Robust estimation on a parametric model via testing",
  "authors": [
    "Mathieu Sart"
  ],
  "comment": "Published at http://dx.doi.org/10.3150/15-BEJ706 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)",
  "journal": "Bernoulli 2016, Vol. 22, No. 3, 1617-1670",
  "doi": "10.3150/15-BEJ706",
  "categories": [
    "math.ST",
    "stat.TH"
  ],
  "abstract": "We are interested in the problem of robust parametric estimation of a density from $n$ i.i.d. observations. By using a practice-oriented procedure based on robust tests, we build an estimator for which we establish non-asymptotic risk bounds with respect to the Hellinger distance under mild assumptions on the parametric model. We show that the estimator is robust even for models for which the maximum likelihood method is bound to fail. A numerical simulation illustrates its robustness properties. When the model is true and regular enough, we prove that the estimator is very close to the maximum likelihood one, at least when the number of observations $n$ is large. In particular, it inherits its efficiency. Simulations show that these two estimators are almost equal with large probability, even for small values of $n$ when the model is regular enough and contains the true density.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-09-09T16:24:51.000Z",
      "title": "Robust estimation on a parametric model with tests",
      "abstract": "We are interested in the problem of robust parametric estimation of a density from i.i.d observations. By using a practice-oriented procedure based on robust tests, we build an estimator for which we establish non-asymptotic risk bounds with respect to the Hellinger distance under mild assumptions on the parametric model. We prove that the estimator is robust even for models for which the maximum likelihood method is bound to fail. We also evaluate the performance of the estimator by carrying out numerical simulations for which we observe that the estimator is very close to the maximum likelihood one when the model is regular enough and contains the true underlying density.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2016-03-30T10:56:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "parametric model",
      "robust estimation",
      "maximum likelihood method",
      "establish non-asymptotic risk bounds",
      "robust parametric estimation"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1308.2927S"
    }
  }
}