An Asymptotically Efficient Solution to the Bandwidth Problem of Kernel Density Estimation

Abstract

A data-driven method of choosing the bandwidth, $h$, of a kernel density estimator is heuristically motivated by considering modifications of the Kullback-Leibler or pseudo-likelihood cross-validation function. It is seen that this means of choosing $h$ is asymptotically equivalent to taking the $h$ that minimizes some compelling error criteria such as the average squared error and the integrated squared error. Thus, for a given kernel function, the bandwidth can be chosen optimally without making precise smoothness assumptions on the underlying density.