  Kernel smooth is the most fundamental technique for data density and
regression estimation. However, time-consuming is the biggest obstacle for the
application that the direct evaluation of kernel smooth for $N$ samples needs
${O}\left( {{N}^{2}} \right)$ operations. People have developed fast smooth
algorithms using the idea of binning with FFT. Unfortunately, the accuracy is
not controllable, and the implementation for multivariable and its bandwidth
selection for the fast method is not available. Hence, we introduce a new
MATLAB toolbox for fast multivariate kernel regression with the idea of
non-uniform FFT (NUFFT), which implemented the algorithm for $M$ gridding
points with ${O}\left( N+M\log M \right)$ complexity and accuracy
controllability. The bandwidth selection problem utilizes the Fast Monte-Carlo
algorithm to estimate the degree of freedom (DF), saving enormous
cross-validation time even better when data share the same grid space for
multiple regression. Up to now, this is the first toolbox for fast-binning
high-dimensional kernel regression. Moreover, the estimation for local
polynomial regression, the conditional variance for the heteroscedastic model,
and the complex-valued datasets are also implemented in this toolbox. The
performance is demonstrated with simulations and an application on the
quantitive EEG.
