Seminar Abstract:

A new method of bandwidth selection for kernel density estimators will be presented. The method, termed indirect crossvalidation (ICV), makes use of socalled selection kernels. Leastsquares crossvalidation (LSCV) is used to select the bandwidth of a selectionkernel estimator and this bandwidth is appropriately rescaled for use in a Gaussian kernel estimator. The proposed selection kernels are linear combinations of two Gaussian kernels and need not be unimodal or positive. A theory is developed showing that the relative error of ICV bandwidths can converge to 0 at a rate of n^{−1/4,} which is substantially better than the n^{−1/10} rate of LSCV. Interestingly, the selection kernels that are best for purposes of bandwidth selection are very poor if used to actually estimate the density function. This property appears to be part of the larger and welldocumented paradox to the effect that "the harder the estimation problem, the better cross validation performs." The ICV method uniformly outperforms LSCV in a simulation study, a real data example, and a simulated example in which bandwidths are chosen locally.
