{
  "id": "0908.1045",
  "version": "v1",
  "published": "2009-08-07T13:05:34.000Z",
  "updated": "2009-08-07T13:05:34.000Z",
  "title": "Asymptotic normality of plug-in level set estimates",
  "authors": [
    "David M. Mason",
    "Wolfgang Polonik"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/08-AAP569 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Applied Probability 2009, Vol. 19, No. 3, 1108-1142",
  "doi": "10.1214/08-AAP569",
  "categories": [
    "math.PR"
  ],
  "abstract": "We establish the asymptotic normality of the $G$-measure of the symmetric difference between the level set and a plug-in-type estimator of it formed by replacing the density in the definition of the level set by a kernel density estimator. Our proof will highlight the efficacy of Poissonization methods in the treatment of large sample theory problems of this kind.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-08-07T13:05:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05",
      "60F15",
      "62E20",
      "62G07"
    ],
    "keywords": [
      "plug-in level set estimates",
      "asymptotic normality",
      "large sample theory problems",
      "kernel density estimator",
      "poissonization methods"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0908.1045M"
    }
  }
}