Abstract
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 $\tilde{S}$ actually used, the Frobenius norm of $S - \tilde{S}$, where $S$ is the correct covariance matrix, and the basis matrix $\phi$. 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.
Citation
Otto Neall Strand. "Coefficient Errors Caused by Using the Wrong Covariance Matrix in the General Linear Model." Ann. Statist. 2 (5) 935 - 949, September, 1974. https://doi.org/10.1214/aos/1176342815
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