부산대학교 도서관

In this paper, sufficient conditions are obtained to prove that the exact mean integrated square error of a density kernel estimator admits a minimizer $h_{0, n}(f)$. It is natural to ask whether or not the minimizer sequence $(h_{0, n}(f))_n$ satisfies the standard limit conditions $h_{0, n}(f) \to 0$ and $n h_{0, n}(f) \to \infty$ as $n\to \infty$. The second one is proved to hold quite generally while the first one does not necessarily hold. In fact, the limit of the minimizer sequence could be strictly positive in some special cases. Both of them are illustrated when using super kernels or the sinc kernel for some particular density classes. As a consequence, superoptimal rates of convergence are achieved and a global zero-bias bandwidth can be selected as shown by simulations.