Stepwise variable selection and maximum likelihood estimation of smoothing factors of kernel functions for nonparametric discriminant functions evaluated by different criteria

Abstract

Kernel functions are used to estimate the probability density functions of variables for nonparametric discriminant analysis. In connection with stepwise variable identification a stepwise maximum likelihood estimation procedure for the estimation of smoothing factors of the kernel functions is developed. This procedure allows a step-by-step estimation of smoothing factors for every variable which is considered to be added to the model or which is examined to substitute a variable in a model. Different criteria for model evaluation in stepwise discriminant analysis are discussed. Beside criteria, like distance and dependence functions and the error and nonerror rate, a criterion which considers the ratio of probability densities of different classes at point x is proposed for stepwise variable identification. An application of the procedures described in this study to a medical decision problem shows the importance of stepwise parameter estimation of kernel functions for nonparametric discriminant analysis and the role of different model evaluation criteria for the selection of the best subset of variables.