Modifying the double smoothing bandwidth selector in nonparametric regression

Abstract

In this paper a modified double smoothing bandwidth selector, ^h MDS , based on a new criterion, which combines the plug-in and the double smoothing ideas, is proposed. A self-complete iterative double smoothing rule ( ^ h IDS ) is introduced as a pilot method. The asymptotic properties of both ^ h IDS and ^ h MDS are investigated. It is shown that ^ h MDS performs asymptotically very well. Moreover, it is asymptotically negatively correlated with h ASE , the minimizer of the averaged squared error. The asymptotic performances of ^ h MDS and of the iterative plug-in method, ^ h IPL (Gasser et al., 1991) are compared. A comparative simulation study is carried out to show the practical performance of ^ h MDS and related methods. It is shown that ^ h MDS seems to be the best in the practice. Finite sample negative correlations between the chosen bandwidth selectors and h ASE are also studied.