Wavelet Density Estimators in Discriminant Analysis

The purpose of discriminant analysis is to predict group membership of an individual on the basis of a set of measurements that have been made on it. In this goal, the availability of a learning sample, for which it is know where each individual came from, is assumed. In this context, the thresholded wavelet density estimator may capture more easily fine structures of group differences than usual linear density estimators (such as kernel-based methods). This does not apply ``as is'' in high dimensional space. However, in the univariate case, the estimator behaves well, and can, therefore, be used in the framework of Projection Pursuit Discriminant Analysis, a method that searches for the one-dimension projection that best separates the groups.