A Complete Efficient FFT-Based Algorithm for Nonparametric Kernel Density Estimation

Multivariate kernel density estimation (KDE) is a very important statistical technique in exploratory data analysis. Research on high performance KDE is still an open research problem. One of the most elegant and efficient approach utilizes the Fast Fourier Transform. Unfortunately, the existing FFT-based solution suffers from a serious limitation, as it can accurately operate only with the constrained (i. e., diagonal) multivariate bandwidth matrices. In the paper we propose a crucial improvement to this algorithm which results in relaxing the above mentioned limitation. Numerical simulation study demonstrates good properties of the new solution.