Classifier selection from a totally bounded class of functions

This article deals with the two-class classification problem, where the class conditional probability pi (x)=P(Y=I / X=x) belongs to some known class of functions F. Given a data-based skeleton estimate F-n, of the class F, with respect to the empirical L-1-norm, we consider methods of constructing classifiers using the members of the class F-n. Conditions under which the resulting classification rules are strongly Bayes consistent are also studied. The results are nonparametric and continue to hold regardless of the VC dimension of the corresponding class of classifiers. (C) 2001 Elsevier Science B.V. All rights reserved.