On the Amount of Noise Inherent in Bandwidth Selection for a Kernel Density Estimator

Abstract

In the setting of kernel density estimation, data-driven bandwidth, i.e., smoothing parameter, selectors are considered. It is seen that there is a well-defined, and surprisingly restrictive, bound on the rate of convergence of any automatic bandwidth selection method to the optimum. The method of least squares cross-validation achieves this bound.

Locations

• The Annals of Statistics - View - PDF