Modifying the double smoothing bandwidth selector in nonparametric regression

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 perfor- mance 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.