On cross-validation for discrete kernel estimates in discrimination

The choice of smoothing determines the properties of nonparametric estimates of probability densities. In the discrimination problem, the choice is often tied to loss functions. A framework for the cross–validatory choice of smoothing parameters based on general loss functions is given. Several loss functions are considered as special cases. In particular, a family of loss functions, which is connected to discrimination problems, is directly related to measures of performance used in discrimination. Consistency results are given for a general class of loss functions which comprise this family of discriminant loss functions.