The Annals of Statistics

Global identifiability of linear structural equation models

Mathias Drton, Rina Foygel, and Seth Sullivant

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Abstract

Structural equation models are multivariate statistical models that are defined by specifying noisy functional relationships among random variables. We consider the classical case of linear relationships and additive Gaussian noise terms. We give a necessary and sufficient condition for global identifiability of the model in terms of a mixed graph encoding the linear structural equations and the correlation structure of the error terms. Global identifiability is understood to mean injectivity of the parametrization of the model and is fundamental in particular for applicability of standard statistical methodology.

Article information

Source
Ann. Statist., Volume 39, Number 2 (2011), 865-886.

Dates
First available in Project Euclid: 9 March 2011

Permanent link to this document
https://projecteuclid.org/euclid.aos/1299680957

Digital Object Identifier
doi:10.1214/10-AOS859

Mathematical Reviews number (MathSciNet)
MR2816341

Zentralblatt MATH identifier
1215.62052

Subjects
Primary: 62H05: Characterization and structure theory 62J05: Linear regression

Keywords
Covariance matrix Gaussian distribution graphical model multivariate normal distribution parameter identification structural equation model

Citation

Drton, Mathias; Foygel, Rina; Sullivant, Seth. Global identifiability of linear structural equation models. Ann. Statist. 39 (2011), no. 2, 865--886. doi:10.1214/10-AOS859. https://projecteuclid.org/euclid.aos/1299680957


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