Practical performance of several data driven bandwidth selectors

Most recently proposed bandwidth selectors in kernel density estimation have been developed with intent to reduce the large sampling variability of Least Squares Cross-Validation. Their asymptotic superiority has been shown in many papers. Some of those selectors have even the fastest n-1/ 2 relative rate of convergence to their theoretical optimum. The aim of this paper is to see what is happening for small sample sizes. Several recently proposed methods of bandwidth selection are considered. These methods are compared to Least Squares Cross-Validation through simulations. Some qualitative measures of performance as well as quantitative ones are used for this comparison. It is seen that, while most of the bandwidth selectors gain some in terms of variance reduction, some of them lose a lot in terms of increased bias resulting in inferior overall performance when compared to Least Squares Cross-Validation.