A0425
Title: Higher-order asymptotic properties of the kernel density estimator with plug-in bandwidth
Authors: Yoshihiko Nishiyama - Kyoto University (Japan) [presenting]
Shunsuke Imai - Kyoto University - Graduate School of Economics (Japan)
Abstract: The effect of bandwidth selection is investigated via the plug-in method on the asymptotic structure of the nonparametric kernel density estimator. We find that the plug-in method has no effect on the asymptotic structure of the estimator up to the order of $O{(nh_0)^{1/2}}= O(n^{L/(2L+1)})$ for a bandwidth $h_0$ and any kernel order $L$. We also provide the valid Edgeworth expansion up to the order of $O{(nh_0)^{-1}}$ and find that the plug-in method starts to have an effect on the term whose convergence rate is $O{(nh_0)^{-1/2}*h0}= O(n^{(L+1)/(2L+1)})$. In other words, we derive the exact convergence rate of the deviation between the distribution functions of the estimator with a deterministic bandwidth and with the plug-in bandwidth. Monte Carlo experiments are conducted to see whether our approximation improves previous results.
