A Modern Gauss–Markov Theorem
给出了线性回归系数无偏估计的有限样本效率下界，证明高斯-马尔可夫定理可去掉线性估计的限制，最小二乘估计和广义最小二乘估计实际上是最佳无偏估计。
This paper presents finite‐sample efficiency bounds for the core econometric problem of estimation of linear regression coefficients. We show that the classical Gauss–Markov theorem can be restated omitting the unnatural restriction to linear estimators, without adding any extra conditions. Our results are lower bounds on the variances of unbiased estimators. These lower bounds correspond to the variances of the the least squares estimator and the generalized least squares estimator, depending on the assumption on the error covariances. These results show that we can drop the label “linear estimator” from the pedagogy of the Gauss–Markov theorem. Instead of referring to these estimators as BLUE, they can legitimately be called BUE (best unbiased estimators).