Robust designs for multivariate polynomial regression on the d-cube

Abstract

For the multivariate polynomial regression model of degree n ∈ N we determine the model robust designs in the sense of Läuter ( Math. Operat. Statist. , 1974) within the class of product measures on the d -cube. The optimal product design is completely described by its canonical moments. The results hold for all d isin; N , n ∈ N and can be generalized to the case that the exponents of the components x 1 ,…, x d in the multivariate polynomial are either of odd or even order. As special cases we give explicit representations of the support points and the weights of the D- and D 1 -optimal product designs for the polynomial which components x 1 ,…, x d appear either with odd or even exponents.