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

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dc.creatorClarkson, Eric
dc.creatorDenny, J. L.
dc.creatorShepp, Larry
dc.date2009-03-03
dc.date.accessioned2026-07-07T12:48:40Z
dc.date.available2026-07-07T12:48:40Z
dc.descriptionFor 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).
dc.descriptionPublished in at http://dx.doi.org/10.1214/08-AAP536 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/0903.0518
dc.identifierhttp://arxiv.org/abs/0903.0518
dc.identifierAnnals of Applied Probability 2009, Vol. 19, No. 1, 467-476
dc.identifierdoi:10.1214/08-AAP536
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/222136
dc.subjectProbability
dc.subject62G32, 60E15 (Primary) 92C55. (Secondary)
dc.titleROC and the bounds on tail probabilities via theorems of Dubins and F. Riesz
dc.typetext

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