Open Access
March, 1984 Estimating Linear Statistical Relationships
T. W. Anderson
Ann. Statist. 12(1): 1-45 (March, 1984). DOI: 10.1214/aos/1176346390


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.


Download Citation

T. W. Anderson. "Estimating Linear Statistical Relationships." Ann. Statist. 12 (1) 1 - 45, March, 1984.


Published: March, 1984
First available in Project Euclid: 12 April 2007

zbMATH: 0542.62039
MathSciNet: MR733497
Digital Object Identifier: 10.1214/aos/1176346390

Primary: 62H12
Secondary: 62H25

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

Rights: Copyright © 1984 Institute of Mathematical Statistics

Vol.12 • No. 1 • March, 1984
Back to Top