On the Plug-in Bandwidth Selectors in Kernel Density Estimation

A stronger result than that of Park and Marron (1994) is proved here on the asymptotic distribution of the plug-in bandwidth selector. The new result is that the plug-in bandwidth selector may have the rate of convergence ($n^{-4/13}$ with less smoothness conditions on the unknown density functions than as described in Park and Marron's paper. Together with this, a class of various plug-in bandwidth selectors are considered and their asymptotic distributions are given. Finally, some ideas of possible improvements on those plug-in bandwidth selectors are provided.