Numerical computation of optimal approximate designs in polynomial spline regression

While polynomial regression models on a one-dimensional interval have received broad attention in optimal design theory, few work has been done on smooth piecewise polynomial regression (polynomial spline regression). This is somewhat contrary to the fact that low degree polynomial splines are widely used in numerical approximation and interpolation. The paper presents algorithms for computing optimal approximate designs for polynomial spline models on a compact interval with fixed nodes. The algorithms are of Newton and Quasi-Newton type as established basically by Gaffke and Heiligers (1996). The optimality criteria considered are Kiefer's #PHI#_p-criteria including the D- and A-criterion, the class of L-criteria, and mixtures of these. The non-smooth E-criterion is approximately included as #PHI#_p, for a small (negative) p. Except for the D-criterion, design optimality depends on the particular choice of the basis of the spline function space. We are dealing with B-splines, which are known to be favourable for numerical purposes, but we also consider the truncated power basis which might appear to be more natural. (orig.)SIGLEAvailable from TIB Hannover: RR 4487(1997,11) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman