ROC and the bounds on tail probabilities via theorems of dubins and f. Riesz

Eric Clarkson, J. L. Denny, Larry Shepp

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

For independent X and Y in the inequality P(X ≤ Y + μ), 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 R Riesz. The inequality was motivated by medical imaging: find bounds on the area under the Receiver Operating Characteristic curve (ROC).

Original languageEnglish (US)
Pages (from-to)467-476
Number of pages10
JournalAnnals of Applied Probability
Volume19
Issue number1
DOIs
StatePublished - Feb 2009

Keywords

  • Extreme points
  • ROC
  • Symmetric rearrangements
  • Tail probabilities

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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