{
  "id": "0708.2180",
  "version": "v1",
  "published": "2007-08-16T13:56:14.000Z",
  "updated": "2007-08-16T13:56:14.000Z",
  "title": "A nonparametric approach to the estimation of lengths and surface areas",
  "authors": [
    "Antonio Cuevas",
    "Ricardo Fraiman",
    "Alberto Rodríguez-Casal"
  ],
  "comment": "Published at http://dx.doi.org/10.1214/009053606000001532 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Statistics 2007, Vol. 35, No. 3, 1031-1051",
  "doi": "10.1214/009053606000001532",
  "categories": [
    "math.ST",
    "stat.TH"
  ],
  "abstract": "The Minkowski content $L_0(G)$ of a body $G\\subset{\\mathbb{R}}^d$ represents the boundary length (for $d=2$) or the surface area (for $d=3$) of $G$. A method for estimating $L_0(G)$ is proposed. It relies on a nonparametric estimator based on the information provided by a random sample (taken on a rectangle containing $G$) in which we are able to identify whether every point is inside or outside $G$. Some theoretical properties concerning strong consistency, $L_1$-error and convergence rates are obtained. A practical application to a problem of image analysis in cardiology is discussed in some detail. A brief simulation study is provided.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-08-16T13:56:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "62G07",
      "62G20"
    ],
    "keywords": [
      "surface area",
      "nonparametric approach",
      "estimation",
      "brief simulation study",
      "theoretical properties concerning strong consistency"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Institute of Mathematical Statistics",
      "journal": "Ann. Stat."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0708.2180C"
    }
  }
}