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

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

2009-03-03

arxiv.org/abs/0903.0518v1

Annals of Applied Probability 2009, Vol. 19, No. 1, 467-476

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/08-AAP536 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/08-AAP536

For independent $X$ and $Y$ in the inequality $P(X\leq Y+\mu)$, 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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