Coefficient Errors Caused by Using the Wrong Covariance Matrix in the General Linear Model

A method is derived to place an approximate bound on the mean-square error incurred by using an incorrect covariance matrix in the Gauss-Markov estimator of the coefficient vector in the full-rank general linear model. The bound thus obtained is a function of the incorrect covariance matrix S̃ actually used, the Frobenius norm of S - S̃, where S is the correct covariance matrix, and the basis matrix φ. This estimate can therefore be computed from known or easily-approximated data in the usual regression problem. All mathematics related to the method is derived, and numerical examples are presented.