Latent models for cross-covariance
Abstract
We consider models for the covariance between two blocks of variables. Such models are often used in situations where latent variables are believed to present. In this paper we characterize exactly the set of distributions given by a class of models with one-dimensional latent variables. These models relate two blocks of observed variables, modeling only the cross-covariance matrix. We describe the relation of this model to the singular value decomposition of the cross-covariance matrix. We show that, although the model is underidentified, useful information may be extracted. We further consider an alternative parameterization in which one latent variable is associated with each block, and we extend the result to models with r-dimensional latent variables.Download Info
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Bibliographic Info
Article provided by Elsevier in its journal Journal of Multivariate Analysis.
Volume (Year): 97 (2006)
Issue (Month): 1 (January)
Pages: 79-102
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Related research
Keywords: Canonical correlation Latent variables Partial least squares Reduced-rank regression Singular value decomposition;References
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Citations
Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.Cited by:
- Ogasawara, Haruhiko, 2007. "Asymptotic expansions of the distributions of estimators in canonical correlation analysis under nonnormality," Journal of Multivariate Analysis, Elsevier, vol. 98(9), pages 1726-1750, October.
- Haruhiko Ogasawara, 2009. "Asymptotic expansions in the singular value decomposition for cross covariance and correlation under nonnormality," Annals of the Institute of Statistical Mathematics, Springer, vol. 61(4), pages 995-1017, December.
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