{
  "id": "1102.1191",
  "version": "v4",
  "published": "2011-02-06T19:48:40.000Z",
  "updated": "2012-06-10T16:56:10.000Z",
  "title": "Smoothed log-concave maximum likelihood estimation with applications",
  "authors": [
    "Yining Chen",
    "Richard J. Samworth"
  ],
  "comment": "29 pages, 3 figures",
  "journal": "Statist. Sinica. 23 (2013), 1373-1398",
  "doi": "10.5705/ss.2011.224",
  "categories": [
    "math.ST",
    "stat.ME",
    "stat.TH"
  ],
  "abstract": "We study the smoothed log-concave maximum likelihood estimator of a probability distribution on $\\mathbb{R}^d$. This is a fully automatic nonparametric density estimator, obtained as a canonical smoothing of the log-concave maximum likelihood estimator. We demonstrate its attractive features both through an analysis of its theoretical properties and a simulation study. Moreover, we use our methodology to develop a new test of log-concavity, and show how the estimator can be used as an intermediate stage of more involved procedures, such as constructing a classifier or estimating a functional of the density. Here again, the use of these procedures can be justified both on theoretical grounds and through its finite sample performance, and we illustrate its use in a breast cancer diagnosis (classification) problem.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2012-06-10T16:56:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "62G07",
      "62E17",
      "62P10"
    ],
    "keywords": [
      "smoothed log-concave maximum likelihood estimation",
      "applications",
      "smoothed log-concave maximum likelihood estimator",
      "fully automatic nonparametric density estimator"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1102.1191C"
    }
  }
}