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The problem of fast computation of multivariate kernel density estimation(KDE) is still an open research problem. In our view, the existing solutions donot resolve this matter in a satisfactory way. One of the most elegant andefficient approach utilizes the fast Fourier transform. Unfortunately, theexisting FFT-based solution suffers from a serious limitation, as it canaccurately operate only with the constrained (i.e., diagonal) multivariatebandwidth matrices. In this paper we describe the problem and give asatisfactory solution. The proposed solution may be successfully used also inother research problems, for example for the fast computation of the optimalbandwidth for KDE.

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