Having studied three widely differing nonparametric regression estimators, it is perhaps time for a comparative critique. In the authors’ view, the strength of the smoothing spline and sieved estimators derive from the maximum likelihood and/or minimum principles. A weakness is that the estimators are constructed in a global manner, even though the estimators are essentially local (as they should be). Contrast this with kernel estimators, which are nothing if not local. It is thus natural to attempt a synthesis of these two principles in the form of maximum local likelihood estimation. In theory at least, this combines the best of both worlds.