97-11
Numerical Computation of Optimal Approximate Designs in Polynomial Spline Regression
Preprint series: 97-11, Preprints
- MSC:
- 62K05 Optimal designs
- 65U05 Numerical methods in probability and statistics
Abstract: While polynomial regression models on a one-dimensional interval havereceived broad attention in optimal design theory, few work has been doneon smooth piecewise polynomial regression (polynomial spline regression).This is somewhat contrary to the fact that low degree polynomial splinesare widely used in numerical approximation and interpolation. The paperpresents algorithms for computing optimal approximate designs for polyno-mial spline models on a compact interval with fixed nodes. The algorithmsare of Newton and Quasi-Newton type as established basically by Gaffke &Heiligers (1996). The optimality criteria considered are Kiefer\'s \Phi p-criteriaincluding the D- and A-criterion, the class of L-criteria, and mixtures ofthese. The non-smooth E-criterion is approximately included as \Phi p, for asmall (negative) p. Except for the D-criterion, design optimality depends onthe particular choice of the basis of the spline function space. We are dealingwith B-splines, which are known to be favourable for numerical purposes,but we also consider the truncated power basis which might appear to bemore natural.