On the Bias and Variance of FFT-Based Kernel Density Estimation

摘要

An efficient computational procedure for kernel density estimation using the FFT algorithm has been given by Silverman. This procedure requires the empirical function to be interpolated on a regular mesh, and the high-frequency interpolation errors can result in a significant loss of accuracy when the kernel density estimates or its derivatives are used as a part of some larger statistical procedure. In this paper, we describe systematic finite element discretization procedures for improving the accuracy of the FFT-based algorithms. We derive the bias and variance of the FFT-based kernel density estimates, and suggest modifications to eliminae interpolation bias. Simulation studies that verify the results of the analysis are presented.