A Constrained Least Squares Approach to the General Gauss-Markov Linear Model
Stavros Kourouklis, Christopher C. Paige · Journal of the American Statistical Association · 1981
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.