Fast optimal bandwidth selection for kernel density estimation

We propose a computationally efficient ϵ−exact approxima-tion algorithm for univariate Gaussian kernel based density
derivative estimation that reduces the computational com-
plexity from O(MN) to linear O(N +M). We apply the pro-
cedure to estimate the optimal bandwidth for kernel density
estimation. We demonstrate the speedup achieved on this
problem using the ”solve-the-equation plug-in” method, and
on exploratory projection pursuit techniques.