A Constrained Least Squares Approach to the General Gauss-Markov Linear Model
将一般高斯-马尔可夫模型中的参数估计转化为约束最小二乘问题，直接得到最佳线性无偏估计，算法数值稳定性优于广义逆方法。
Abstract The task of estimating the vector of parameters β in the general Gauss-Markov model (y, Xβ, σ2 W) with no restrictions on the design matrix X or the covariance matrix σ2 W is formulated as a constrained linear least squares problem. A BLUE of any estimable function of β is obtained directly by solving this problem. The use of matrix decompositions leads to numerically stable algorithms for computing the solution. The approach is theoretically easy and is shown to be computationally more sound than methods based on generalized inverses. Practical expressions for the desired estimators, their covariance matrices, and an estimator of σ2 are given. Key Words: General Gauss-Markov linear modelConstrained least squaresCovariance matrixGeneralized inverseNumerical stability