A note on minimax robustness of designs against correlated or heteroscedastic responses

We present a result according to which certain functions of covariance matrices are maximized at scalar multiples of the identity matrix. This is used to show that experimental designs that are optimal under an assumption of independent, homoscedastic responses can be minimax robust, in broad classes of alternate covariance structures. In particular, it can justify the common practice of disregarding possible dependence, or heteroscedasticity, at the design stage of an experiment.