Distribution - free performance bounds with the I resubstitution error estimate

Gascuel, O. and G. Caraux, Distribution-free performance bounds with the resubstitution error estimate, Pattern Recognition Letters 13 (1992) 757-764. Two distribution-free upper bounds are given for the true error rate of a classifier, using the resubstitution error estimate. These bounds apply when the classifier is selected from a finite decision rule set. Both improve a bound proposed by Vapnik (1982). One of them is in a way optimal, while however presenting the disadvantage to be not analytic and requiring to be computed numerically for a given situation. A quantitative comparison of these bounds is provided, with realistic parameter values taken from classification trees and histogram discrimination rules.