Modifying the double smoothing bandwidth selector in nonparametric regression

In this paper a modified double smoothing bandwidth selector, hˆMDS, based on a new criterion defined as the sum of the asymptotic variance and the squared double smoothing bias, is proposed. A self-contained iterative double smoothing rule (hˆIDS) is introduced as a pilot method. The asymptotic properties of hˆIDS and hˆMDS are investigated. It is shown that asymptotically hˆMDS performs very well. The asymptotic performance of hˆMDS is also compared with plug-in bandwidth selectors. A comparative simulation study is carried out to show the practical performance of hˆMDS and related methods, including ordinary double smoothing and two plug-in bandwidth selectors. The results indicate that hˆMDS tends to be the best in practice.