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).
Clarkson
Eric
E
College of Optical Sciences, Department of Radiology, University of Arizona, Tucson, Arizona 85721, USA, clarkson@radiology.arizona.edu.
Denny
J L
JL
Shepp
Larry
L