ROC and the bounds on tail probabilities via theorems of Dubins and F. Riesz release_635g56rppfdsvnkmjkls3cly5y

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

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2009  

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 F. Riesz. The inequality was motivated by medical imaging: find bounds on the area under the Receiver Operating Characteristic curve (ROC).
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Type  report
Stage   submitted
Date   2009-03-03
Version   v1
Language   en ?
Number  IMS-AAP-AAP536
arXiv  0903.0518v1
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