FFT-Based Fast Computation of Multivariate Kernel Estimators with Unconstrained Bandwidth Matrices

The problem of fast computation of multivariate density estimation is still an open research problem. In our view, the existing solutions don't resolve this matter in a satisfactory way. One of the most elegant and efficient approach utilizes fast Fourier transform. Unfortunately, the existing FFT-based solution suffers a serious bottleneck, as it can accurately operate only with constrained (that is diagonal) multivariate bandwidth matrices. This seams a quite serious limitation. In this paper we describe the problem and give a satisfactory solution.