Robustness of A-optimal designs

Suppose that Y=(Yi) is a normal random vector with mean Xb and covariance σ2In, where b is a p-dimensional vector (bj),X=(Xij) is an n×p matrix. A-optimal designs X are chosen from the traditional set D of A-optimal designs for ρ=0 such that X is still A-optimal in D when the components Yi are dependent, i.e., for i≠i′, the covariance of Yi,Yi′ is ρ with ρ≠0. Such designs depend on the sign of ρ. The general results are applied to X=(Xij), where Xij∈{-1,1}; this corresponds to a factorial design with -1,1 representing low level or high level respectively, or corresponds to a weighing design with -1,1 representing an object j with weight bj being weighed on the left and right of a chemical balance respectively.