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.

翻译：我们提出一个结果：协方差矩阵的某些函数在标量倍的单位矩阵处取最大值。这一结论用于证明，在假定响应独立同方差的条件下最优的实验设计，可在广泛的替代协方差结构类中具有极小极大鲁棒性。特别地，这为实验设计阶段忽视可能存在的相关性或异方差性的常见做法提供了理论依据。