An alternative choice of smoothing for kernel-based density estimates in discrete discriminant analysis

Abstract

The kernel method of estimating the cell probabilities of a multivariate categorical distribution, due to Aitchison & Aitken (1976), depends crucially on an unknown smoothing parameter λ. A method of estimating A is introduced which is explicitly connected to multivariate discrimination. The method, based on maximization of the leaving-one-out estimator of the nonerror rate, is shown to be Bayes risk strongly consistent. An example is given to illustrate the application.