The most important factor in multivariate kernel density estimation is a choice of a bandwidth matrix. This choice is particularly important, because of its role in controlling both the amount and the direction of multivariate smoothing. Considerable attention has been paid to constrained...

Nonparametric density estimators on RK may fail to be consistent when the sample size n does not grow fast enough relative to reduction in smoothing. For example a Gaussian kernel estimator with bandwidths proportional to some sequence hn is not consistent if nhnK fails to diverge to infinity....