Kernel Density Estimation: Theory and Application in Discriminant Analysis

Abstract

Nowadays, one can find a huge set of methods to estimate the density function of a random variable nonparametrically. Since the first version of the most elementary nonparametric density estimator (the histogram) researchers produced a vast amount of ideas especially corresponding to the issue of choosing the bandwidth parameter in a kernel density estimator model. To focus not only on a descriptive application, the model seems to be quite suitable for application in discriminant analysis, where (multivariate) class densities are the basis for the assignment of a vector to a given class. Thisarticle gives insight to most popular bandwidth parameter selectors as well as to the performance of the kernel density estimator as a classification method compared to the classical linear and quadratic discriminant analysis, respectively. Both a direct estimation in a multivariate space as well as an application of the concept to marginal normalizations of the single variables will be taken into consideration. From this report the gap between theory and application is going to be pointed out.