ON PARTIAL LOCAL SMOOTHING RULES FOR CURVE ESTIMATION

We compare the performances of local and global rules for smoothing pa rameter choice, in terms of asymptotic mean squared errors of the resu lting estimators. In some instances there is surprisingly little to ch oose between local and global approaches; our analysis identifies cont exts where the differences are small or large. This work motivates dev elopment of smoothing rules that form a 'half-way house' between local and global smoothing. There, interpolation provides a basis for parti al local smoothing. A key result shows that interpolation on even a co arse grid can produce a very good approximation to full local smoothin g. Our theoretical and numerical results lead us to suggest linear int erpolation of a bandwidth obtained by integral approximations on discr ete intervals.