Fast implementations of nonparametric curve estimators

Recent proposals for implementation of kernel based nonparametric curve estimators are seen to be faster than naive direct implementations by factors up into the hundreds. The main ideas behind two different approaches of this type are made clear. Careful speed comparisons in a variety of settings, and using a variety of machines and software is done. Various issues on computational accuracy and stability are also discussed. The fast methods are seen to be somewhat better than methods traditionally considered very fast, such as LOWESS and smoothing splines.