A simple root n bandwidth selector for nonparametric regression

The purpose of this paper is to investigate data-driven bandwidth selection for nonparametric regression based on a double-smoothing procedure. It will be shown that the best convergence rate can be achieved by kernel regression with non-negative kernels in both pilot smoothing and as well as in main smoothing. The asymptotic results are given for a naive kernel estimator with an equally spaced design, but they can also be used for other kernel estimators or for locally weighted regression. Three variates of data-driven bandwidth selectors for local linear regression are proposed. One of them, (h) over cap(DS1), is root n consistent. The performance of these bandwidth selectors is studied through simulation. They are also compared with the bandwidths selected by the R criterion of Rice and the true ASE optimal bandwidth (h(ASE)) In spite of satisfactory performances of all bandwidth selectors, the root n one turns out to be the best in theory as well as in practice.