{
  "id": "0903.0518",
  "version": "v1",
  "published": "2009-03-03T12:41:50.000Z",
  "updated": "2009-03-03T12:41:50.000Z",
  "title": "ROC and the bounds on tail probabilities via theorems of Dubins and F. Riesz",
  "authors": [
    "Eric Clarkson",
    "J. L. Denny",
    "Larry Shepp"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/08-AAP536 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Applied Probability 2009, Vol. 19, No. 1, 467-476",
  "doi": "10.1214/08-AAP536",
  "categories": [
    "math.PR"
  ],
  "abstract": "For independent $X$ and $Y$ in the inequality $P(X\\leq Y+\\mu)$, we give sharp lower bounds for unimodal distributions having finite variance, and sharp upper bounds assuming symmetric densities bounded by a finite constant. The lower bounds depend on a result of Dubins about extreme points and the upper bounds depend on a symmetric rearrangement theorem of F. Riesz. The inequality was motivated by medical imaging: find bounds on the area under the Receiver Operating Characteristic curve (ROC).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-03-03T12:41:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "62G32",
      "60E15",
      "92C55"
    ],
    "keywords": [
      "tail probabilities",
      "upper bounds assuming symmetric densities",
      "lower bounds",
      "bounds depend"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.0518C"
    }
  }
}