Criterion-Robust Experimental Designs for the Quadratic Regression on a Square and a Cube

Consider the quadratic regression model on the q-dimensional cube [1, 1](q). The purpose of this article is to exhibit designs for the quadratic regression that are criterion robust in the sense of maximin efficiency within the class of all orthogonally invariant information functions. For the case of the standard quadratic regression on an interval (q=1), the asymptotic maximin efficient design is already known. In this article, we give the asymptotic maximin efficient design analytically for q=2, and numerically for q=3. Moreover, for both q=2 and q=3, we compute the measures of criterion-robustness of the D-, E-, and A-optimal designs, and propose criterion robust exact designs of sizes up to 44. Our results suggest that the A-optimal design is particularly efficiency-robust under all orthogonally invariant information functions.