THREE RANK FORMULAS ASSOCIATED WITH THE COVARIANCE MATRICES OF THE BLUE AND THE OLSE IN THE GENERAL LINEAR MODEL
研究一般线性模型中普通最小二乘估计和最佳线性无偏估计的协方差矩阵之差的秩，给出新的简洁表达式，并推导两者相等的条件。
In this paper we consider the estimation of the expectation vector X β under the general linear model { y , X β,σ 2 V }. We introduce a new handy representation for the rank of the difference of the covariance matrices of the ordinary least squares estimator OLSE( X β) (= Hy , say) and the best linear unbiased estimator BLUE( X β) (= Gy , say). From this formula some well-known conditions for the equality between Hy and Gy follow at once. We recall that the equality between Hy and Gy can be characterized by the rank-subtractivity ordering between the covariance matrices of y and Hy . This rank characterization suggests a particular presentation for the rank of the difference of the covariance matrices of Hy and Gy . We show, however, that this presentation is valid if and only if the model is connected.