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April 2011 Global identifiability of linear structural equation models
Mathias Drton, Rina Foygel, Seth Sullivant
Ann. Statist. 39(2): 865-886 (April 2011). DOI: 10.1214/10-AOS859


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.


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Mathias Drton. Rina Foygel. Seth Sullivant. "Global identifiability of linear structural equation models." Ann. Statist. 39 (2) 865 - 886, April 2011.


Published: April 2011
First available in Project Euclid: 9 March 2011

zbMATH: 1215.62052
MathSciNet: MR2816341
Digital Object Identifier: 10.1214/10-AOS859

Primary: 62H05 , 62J05

Keywords: Covariance matrix , Gaussian distribution , Graphical model , multivariate normal distribution , parameter identification , structural equation model

Rights: Copyright © 2011 Institute of Mathematical Statistics


Vol.39 • No. 2 • April 2011
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