Efficient \(D_ s\)-optimal designs for multivariate polynomial regression on the q-cube (Q1115068)

This is a paper within the classical world of KIEFER's optimal experimental design. Approximate \(D_ s\)-optimal designs for polynomial regression in q variables of degree n on the q-dimensional unit-cube are considered. Especially, for \(n=2\) a complete description of the \(D_ s\)- optimal designs for estimating only the quadratic terms is given. For \(n=3,4,5\) and \(q=2,3\) numerical results are presented which support the general idea that D- and \(D_ s\)-optimal designs are ``close to'' product designs. Therefore, in the last section, \(D_ s\)-optimal product designs are described by use of canonical moments and, indeed, they show high efficiencies.