A Nonlinear Version of the Gauss-Markov Theorem
本文在线性回归模型中证明，对于一类非线性估计量，其风险矩阵的下界等于高斯-马尔可夫估计量的协方差矩阵，前提是误差项服从椭圆对称分布。
Abstract This article gives a nonlinear version of the Gauss—Markov theorem. It is shown that in a linear regression model y = Xβ + u, the lower bound for the risk matrix of a nonlinear estimator of β belonging to a certain class is the covariance matrix of the Gauss—Markov estimator, provided the distribution of error term u belongs to the class of elliptically symmetric distributions with second moments.