Improvement of a data based bandwidth selector

A recently proposed data based method for choosing the bandwidth of a kernel density estimator is considered. Intuitive and asymptotic reasons are given for why the selected bandwidth should be smaller than is appropriate. This conflicts with the results of a simulation study. The conflict is resolved through a deeper asymptotic analysis. Further simulation results investigate the issue of what sample sizes are required for the asymptotics to properly describe the situation. The analysis is extended to motivate a remedy, which leads to the widely known least-squares cross-validation, hence providing a new characterization of the latter.