The Annals of Statistics

Estimating Linear Statistical Relationships

T. W. Anderson

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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

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

First available in Project Euclid: 12 April 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 62H12: Estimation
Secondary: 62H25: Factor analysis and principal components; correspondence analysis

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


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

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