Criterion-robust designs for the models of spring balance weighing

In the paper we consider the linear regression model of the first degree on the vertices of the d-dimensional unit cube and its extension by an intercept term, which can be used, e.g., to model unbiased or biased weighing of d objects on a spring balance. In both settings, we can restrict our search for approximate optimal designs to the convex combinations of the so-called j-vertex designs. We focus on the designs that are criterion robust in the sense of maximin efficiency within the class of all orthogonally invariant information functions, involving the criteria of D-, A-, E-optimality, and many others. For the model of unbiased weighing, we give analytic formulas for the maximin efficient design, and for the biased model we present numerical results based on the application of the methods of semidefinite programming.