Efficient \(D_ s\)-optimal designs for multivariate polynomial regression on the q-cube. (English) Zbl 0664.62075

Lim, Yong B.; Studden, W. J.

Ann. Stat. 16, No. 3, 1225-1240 (1988).

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.

Reviewer: W.Näther

MSC:

62K05	Optimal statistical designs
62J05	Linear regression; mixed models

Keywords:

approximate D-optimal designs; estimating higher degree terms; efficiency calculations; symmetric designs; q-cube; Ds-optimality; polynomial regression; numerical results; product designs; canonical moments