On partial local smoothing rules for curve estimation

Abstract

SUMMARY We compare the performances of local and global rules for smoothing parameter choice, in terms of asymptotic mean squared errors of the resulting estimators. In some instances there is surprisingly little to choose between local and global approaches; our analysis identifies contexts where the differences are small or large. This work motivates development of smoothing rules that form a ‘half-way house’ between local and global smoothing. There, interpolation provides a basis for partial local smoothing. A key result shows that interpolation on even a coarse grid can produce a very good approximation to full local smoothing. Our theoretical and numerical results lead us to suggest linear interpolation of a bandwidth obtained by integral approximations on discrete intervals.