Multivariate density estimation with optimal marginal parzen density estimation and gaussianization

Multivariate density estimation is an important problem that is frequently encountered in statistical learning and signal processing. One of the most popular techniques is Parzen windowing, also referred to as kernel density estimation. Gaussianization is a procedure that allows one to estimate multivariate densities efficiently from the marginal densities of the individual random variables. In this paper, we present an optimal density estimation scheme that combines the desirable properties of Parzen windowing and Gaussianization, using minimum Kullback-Leibler divergence as the optimality criterion for selecting the kernel size in the Parzen windowing step. The performance of the estimate is illustrated in a classifier design example