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

Eric Clarkson; J. L. Denny; Larry Shepp

doi:10.1214/08-AAP536

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

Eric Clarkson
, J. L. Denny
, Larry Shepp

Medical Imaging

Research output: Contribution to journal › Article › peer-review

5 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 language	English (US)
Pages (from-to)	467-476
Number of pages	10
Journal	Annals of Applied Probability
Volume	19
Issue number	1
DOIs	https://doi.org/10.1214/08-AAP536
State	Published - 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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10.1214/08-AAP536

Cite this

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AB - 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).

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KW - ROC

KW - Symmetric rearrangements

KW - Tail probabilities

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

Abstract

Keywords

ASJC Scopus subject areas

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