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：我们提出了一项结果，根据该结果，协方差矩阵的某些函数在单位矩阵的标量倍数处达到最大值。这被用于证明，在独立、同方差响应的假设下最优的实验设计，在广泛的备选协方差结构类别中可能具有极小极大稳健性。特别地，这可以证明在实验设计阶段忽略可能的相关性或异方差性这一常见做法是合理的。