The Annals of Statistics

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

Otto Neall Strand

Full-text: Open access

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.

Article information

Source
Ann. Statist., Volume 2, Number 5 (1974), 935-949.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176342815

Digital Object Identifier
doi:10.1214/aos/1176342815

Mathematical Reviews number (MathSciNet)
MR356378

Zentralblatt MATH identifier
0293.15022

JSTOR
links.jstor.org

Subjects
Primary: 15A60: Norms of matrices, numerical range, applications of functional analysis to matrix theory [See also 65F35, 65J05]
Secondary: 62F10: Point estimation

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

Citation

Strand, Otto Neall. Coefficient Errors Caused by Using the Wrong Covariance Matrix in the General Linear Model. Ann. Statist. 2 (1974), no. 5, 935--949. doi:10.1214/aos/1176342815. https://projecteuclid.org/euclid.aos/1176342815


Export citation