The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 19, Number 1 (2009), 467-476.
ROC and the bounds on tail probabilities via theorems of Dubins and F. Riesz
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).
Ann. Appl. Probab. Volume 19, Number 1 (2009), 467-476.
First available in Project Euclid: 20 February 2009
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62G32: Statistics of extreme values; tail inference 60E15: Inequalities; stochastic orderings
Secondary: 92C55: Biomedical imaging and signal processing [See also 44A12, 65R10, 94A08, 94A12]
Clarkson, Eric; Denny, J. L.; Shepp, Larry. ROC and the bounds on tail probabilities via theorems of Dubins and F. Riesz. Ann. Appl. Probab. 19 (2009), no. 1, 467--476. doi:10.1214/08-AAP536. http://projecteuclid.org/euclid.aoap/1235140346.