Wild Cross-validation for Density Estimation
Olga Y. Savchuk, Jeffrey D. Hart, Simon J. Sheather
Department of Statistics, Texas A&M University
 
Abstract: A new method of selecting the bandwidth of a kernel density estimator
is proposed. The method, termed wild cross-validation, uses least squares
cross-validation (LSCV) to select the bandwidth of a so-called wild kernel, and
then rescales this bandwidth to be appropriate for use in a Gaussian kernel
estimator. The wild kernels are linear combinations of two Gaussian kernels,
and are wild since they need not be unimodal or positive. We develop theory
showing that the relative error of wild CV bandwidths can converge to 0 at a
rate of n^(-1/4), which is substantially better than the n^(-1/10) rate of LSCV. The
wild CV method uniformly outperforms LSCV in a simulation study and in two
real data examples.

Keywords: Cross-validation; Bandwidth selection; Kernel density estimation.