Indirect Cross-Validation for Density Estimation

A new method of bandwidth selection or kernel density estimators is proposed The method termed indirect cross-validation (ICY). makes use of so-called selection kernels Least-squares cross-validation (LSCV) is used to select the bandwidth of a selection-kernel estimator and this bandwidth is appropriately escaled for use in a Gaussian kernel estimator The proposed selection kernels are linear combinations of two Gaussian kennels 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 die density function This property appears to be part of the lamer and we paradox to the effect that the harder the estimation problem. the better cross-validation performs'. The ICV method urn form outperforms LSCV in a simulation study. a real data example and a simulated example in which bandwidths are chosen locally Supplemental materials for the article available online