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：我们给出一个结果，根据该结果，协方差矩阵的某些函数在恒等矩阵的标量倍数处达到最大值。这一结果用于证明，在独立、同方差响应的假设下最优的实验设计，在广泛的替代协方差结构类中可能具有最小最大稳健性。特别地，它能够为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提供理论依据。