Fast optimal bandwidth selection for kernel density estimation

This is the authors' abstract. We don't add key points for this paper.

We propose a computationally efficient ∊-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.