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arXiv · 0903.0518

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

Eric Clarkson·J. L. Denny·Larry Shepp
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Abstract

For independent $X$ and $Y$ in the inequality $P(X\leq Y+μ)$, 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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Eric Clarkson, J. L. Denny, Larry Shepp. 2009-03-03. ROC and the bounds on tail probabilities via theorems of Dubins and F. Riesz. https://doi.org/10.1214/08-aap536

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