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

Eric W Clarkson, J. L. Denny, Larry Shepp

Research output: Contribution to journalArticle

2 Citations (Scopus)

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

Fingerprint

Tail Probability
Receiver Operating Characteristic Curve
Lower bound
Unimodal Distribution
Upper bound
Medical Imaging
Extreme Points
Rearrangement
Theorem
Receiver operating characteristic curve
Tail probability
Lower bounds
Imaging

Keywords

  • Extreme points
  • ROC
  • Symmetric rearrangements
  • Tail probabilities

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

ROC and the bounds on tail probabilities via theorems of dubins and f. Riesz. / Clarkson, Eric W; Denny, J. L.; Shepp, Larry.

In: Annals of Applied Probability, Vol. 19, No. 1, 02.2009, p. 467-476.

Research output: Contribution to journalArticle

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