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

Computation