On the minimax robustness against correlation and heteroscedasticity of ordinary least squares among generalized least squares estimates of regression
重新审视了协方差矩阵的某些函数在单位矩阵的标量倍数处取最大值的结论，证明了在正确设定的回归模型中，普通最小二乘估计在广义最小二乘估计中具有极小极大性质，并探讨了模型误设和设计均匀性的影响。
Summary We revisit a result according to which certain functions of covariance matrices are maximized at scalar multiples of the identity matrix. In a statistical context in which such functions measure loss, this says that the least favourable form of dependence is in fact independence, so that a procedure optimal for independent and identically distributed data can be minimax. In particular, the ordinary least squares estimate of a correctly specified regression response is minimax among generalized least squares estimates, when the maximum is taken over certain classes of error covariance structures and the loss function possesses a natural monotonicity property. In regression models whose response function is possibly misspecified, ordinary least squares is minimax if the design is uniform on its support, but this often fails otherwise. An investigation of the interplay between minimax generalized least squares procedures and minimax designs leads us to extend, to robustness against dependencies, an existing observation: that robustness against model misspecifications is increased by splitting replicates into clusters of observations at nearby locations.