{
  "id": "2011.07781",
  "version": "v1",
  "published": "2020-11-16T08:24:29.000Z",
  "updated": "2020-11-16T08:24:29.000Z",
  "title": "Normal approximation in total variation for statistics in geometric probability",
  "authors": [
    "Tianshu Cong",
    "Aihua Xia"
  ],
  "comment": "52 pages, 8 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "We use Stein's method to establish the rates of normal approximation in terms of the total variation distance for a large class of sums of score functions of marked Poisson point processes on $\\mathbb{R}^d$. As in the study under the weaker Kolmogorov distance, the score functions are assumed to satisfy stabilizing and moment conditions. At the cost of an additional non-singularity condition for score functions, we show that the rates are in line with those under the Kolmogorov distance. We demonstrate the use of the theorems in four applications: Voronoi tessellation, $k$-nearest neighbours, timber volume and maximal layers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-16T08:24:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05",
      "60D05",
      "60G55",
      "62E20"
    ],
    "keywords": [
      "normal approximation",
      "geometric probability",
      "score functions",
      "statistics",
      "marked poisson point processes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 52,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}