{
  "id": "0911.0331",
  "version": "v1",
  "published": "2009-11-02T15:09:46.000Z",
  "updated": "2009-11-02T15:09:46.000Z",
  "title": "Laws of large numbers and nearest neighbor distances",
  "authors": [
    "Mathew D. Penrose",
    "J. E. Yukich"
  ],
  "comment": "15 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider the sum of power weighted nearest neighbor distances in a sample of size n from a multivariate density f of possibly unbounded support. We give various criteria guaranteeing that this sum satisfies a law of large numbers for large n, correcting some inaccuracies in the literature on the way. Motivation comes partly from the problem of consistent estimation of certain entropies of f.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-11-02T15:09:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60D05",
      "60F25"
    ],
    "keywords": [
      "large numbers",
      "power weighted nearest neighbor distances",
      "multivariate density",
      "sum satisfies",
      "motivation comes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0911.0331P"
    }
  }
}