## The Annals of Statistics

- Ann. Statist.
- Volume 12, Number 1 (1984), 1-45.

### Estimating Linear Statistical Relationships

#### Abstract

This paper on estimating linear statistical relationships includes three lectures on linear functional and structural relationships, factor analysis, and simultaneous equations models. The emphasis is on relating the several models by a general approach and on the similarity of maximum likelihood estimators (under normality) in the different models. In the first two lectures the observable vector is decomposed into a "systematic part" and a random error; the systematic part satisfies the linear relationships. Estimators are derived for several cases and some of their properties given. Estimation of the coefficients of a single equation in a simultaneous equations model is shown to be equivalent to estimation of linear functional relationships.

#### Article information

**Source**

Ann. Statist., Volume 12, Number 1 (1984), 1-45.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176346390

**Digital Object Identifier**

doi:10.1214/aos/1176346390

**Mathematical Reviews number (MathSciNet)**

MR733497

**Zentralblatt MATH identifier**

0542.62039

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62H12: Estimation

Secondary: 62H25: Factor analysis and principal components; correspondence analysis

**Keywords**

Linear functional relations errors in variables linear structural relationships factor analysis canonical variables discriminant analysis structural equations simultaneous equation models multivariate analysis of variance (MANOVA) principal components

#### Citation

Anderson, T. W. Estimating Linear Statistical Relationships. Ann. Statist. 12 (1984), no. 1, 1--45. doi:10.1214/aos/1176346390. https://projecteuclid.org/euclid.aos/1176346390