Approximate [formula omitted]-optimal designs for polynomial models over the unit ball

Abstract

This paper is concerned with approximate I-optimal designs for full polynomial models over the unit ball. The designs have support on an appropriate set of spheres concentric or coincident with the boundary of the unit ball and place weights on the uniform distributions over those spheres. The result is stated in a single sentence in the paper by Galil and Kiefer (1977) but has not been revisited since. The proof indicated by these authors is formalized and the requisite designs are constructed using an approach which emanates from Euclidean design theory. Comparisons of the approximate I-optimal designs with their D-optimal counterparts are made and a Pareto approach to obtaining a design which is a compromise between D- and I-efficiency is introduced. Examples which reinforce the findings are presented throughout.