ADMISSIBLE EXPERIMENTAL-DESIGNS IN MULTIPLE POLYNOMIAL REGRESSION

We give a connection between admissibility of a design in a multiple polynomial setup in v variables and admissibility of subdesigns in multiple setups in less than v variables. This leads to practicable conditions on the support of an admissible design. Especially, for a convex experimental region X an admissible linear regression design is concentrated on the extreme points of X, and an admissible quadratic regression design has at most one support point in the relative interior of an arbitrary face of X. For the ball and the cube we give all admissible (and invariant) linear and quadratic regression designs, proving that the necessary conditions on the support given in Heiligers (1991) are sufficient as well. As demonstrated for both regions, our results substantially reduce the problem of finding optimal designs.