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September, 1974 Coefficient Errors Caused by Using the Wrong Covariance Matrix in the General Linear Model
Otto Neall Strand
Ann. Statist. 2(5): 935-949 (September, 1974). DOI: 10.1214/aos/1176342815

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.

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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

Information

Published: September, 1974
First available in Project Euclid: 12 April 2007

zbMATH: 0293.15022
MathSciNet: MR356378
Digital Object Identifier: 10.1214/aos/1176342815

Subjects:
Primary: 15A60
Secondary: 62F10

Keywords: Covariance matrix , expected mean-square error , incorrect covariances , matrix trace expressions

Rights: Copyright © 1974 Institute of Mathematical Statistics

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Vol.2 • No. 5 • September, 1974
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