A simple root n bandwidth selector for nonparametric regression

The problem of selecting bandwidth for nonparametric regression is investigated. The methodology used here is a double-smoothing procedure with data-driven pilot bandwidths. After giving an extension of the asymptotic result of Hardle, Hall and Marron (1992) by transfering the ideas of Jones, Marron and Park (1991) into the context of nonparametric regression, some fast data-driven bandwidth selectors for nonparametric regression are proposed. One of them, hpsi, is root n consistent. The performance of these bandwidth selectors is studied through simulation for local linear regression. They are also compared with the bandwidth selected by R criterion and the true ASE optimal bandwidth (HASE). Though all of them show a satisfactory performance, the root n bandwidth selector turns out to be the best.