Fast optimal bandwidth selection for kernel density estimation

Abstract

We propose a computationally efficient ε-exact approximation algorithm for univariate Gaussian kernel based density derivative estimation that reduces the computational complexity from O(MN) to linear O(N+M). We apply the procedure 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.