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ROC and the bounds on tail probabilities via theorems of Dubins and F.
Riesz
release_635g56rppfdsvnkmjkls3cly5y
by
Eric Clarkson, J. L. Denny, Larry Shepp
Released
as a report
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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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