Criterion-robust designs for the models of spring balance weighing

Abstract

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. In the paper 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 formulae for the maximin efficient design, and for
the biased model we present numerical results based on the application of the methods of
semidefinite programming.