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The performance of multivariate kernel density estimation (KDE) dependsstrongly on the choice of bandwidth matrix. The high computational costrequired for its estimation provides a big motivation to develop fast andaccurate methods. One of such methods is based on the Fast Fourier Transform.However, the currently available implementation works very well only for theunivariate KDE and it's multivariate extension suffers from a very seriouslimitation as it can accurately operate only with diagonal bandwidth matrices.A more general solution is presented where the above mentioned limitation isrelaxed. Moreover, the presented solution can by easily adopted also for thetask of efficient computation of integrated density derivative functionalsinvolving an arbitrary derivative order. Consequently, bandwidth selection forkernel density derivative estimation is also supported. The practical usabilityof the new solution is demonstrated by comprehensive numerical simulations.

FFT-Based Fast Bandwidth Selector for Multivariate Kernel Density Estimation