## The Annals of Statistics

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

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

#### 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