  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.
