A SIMPLE ROOT-N BANDWIDTH SELECTOR FOR NONPARAMETRIC REGRESSION

The purpose of this paper is to investigate data-driven bandwidth sele ction for nonparametric regression based on a double-smoothing procedu re. It will be shown that the best convergence rate can be achieved by kernel regression with non-negative kernels in both pilot smoothing a nd as well as in main smoothing. The asymptotic results are given for a naive kernel estimator with an equally spaced design, but they can a lso be used for other kernel estimators or for locally weighted regres sion. Three variates of data-driven bandwidth selectors for local line ar regression are proposed. One of them, (h) over cap(DS1), is root n consistent. The performance of these bandwidth selectors is studied th rough 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.