Optimal Design for Moving Local Regressions

This paper describes the so-called moving local regression, a special nonparametric statistical tool, which is firstly discussed thoroughly from analysis point of view. It avoids some drawbacks of its most serious alternatives: spline and kernel methods. The former lack computational simplicity and calculation speed, the latter may introduce high bias due to local constancy. The methods incorporation into the design framework is given, including the derivation of the necessary formulae. A Kiefer-Wolfowitz type equivalence theorem is formulated. Some geometrical examples illuminate the interrelations of the basic ingredients of the method and establish empirical relations to parametric techniques. (author's abstract)