Kernel Density Classification and Boosting

Kernel density estimation is a commonly used approach to classification. However, most of the theoretical results for kernel methods apply to estimation per se and not necessarily to classification. For example, in estimating the difference between two densities, we show that the optimal smoothing parameters are increasing functions of the sample size of the complementary group. A relative newcomer to the classification portfolio is “boosting”, and this paper proposes an algorithm for boosting kernel density classifiers. We note that boosting is closely linked to a previously proposed method of bias reduction in kernel density estimation and indicate how it will enjoy similar properties for classification. Numerical examples and simulations are used to illustrate the findings, and we also suggest further areas of research. Some key words: Cross-validation; Discrimination; Nonparametric Density Estimation; Simulation; Smoothing.