{
  "id": "1903.04663",
  "version": "v1",
  "published": "2019-03-11T23:57:42.000Z",
  "updated": "2019-03-11T23:57:42.000Z",
  "title": "Calibrating dependence between random elements",
  "authors": [
    "Abram M. Kagan",
    "Gabor J. Székely"
  ],
  "categories": [
    "math.PR",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "Attempts to quantify dependence between random elements X and Y via maximal correlation go back to Gebelein (1941) and R\\'{e}nyi (1959). After summarizing properties (including some new) of the R\\'{e}nyi measure of dependence, a calibrated scale of dependence is introduced. It is based on the ``complexity`` of approximating functions of X by functions of Y.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-11T23:57:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H99",
      "62E10"
    ],
    "keywords": [
      "random elements",
      "calibrating dependence",
      "maximal correlation",
      "summarizing properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}