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Post-processing for Bayesian analysis of reduced rank regression models with orthonormality restrictions
Aßmann, Christian; Boysen-Hogrefe, Jens; Pape, Markus (2024): Post-processing for Bayesian analysis of reduced rank regression models with orthonormality restrictions, in: Bamberg: Otto-Friedrich-Universität, S. 577–609.
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Year of publication:
2024
Pages:
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Advances in statistical analysis : AStA, 108 (2024), 3, S. 577-609. - ISSN: 1863-8171, 1863-818X
Year of first publication:
2024
Language:
English
Abstract:
Orthonormality constraints are common in reduced rank models. They imply that matrix-variate parameters are given as orthonormal column vectors. However, these orthonormality restrictions do not provide identification for all parameters. For this setup, we show how the remaining identification issue can be handled in a Bayesian analysis via post-processing the sampling output according to an appropriately specified loss function. This extends the possibilities for Bayesian inference in reduced rank regression models with a part of the parameter space restricted to the Stiefel manifold. Besides inference, we also discuss model selection in terms of posterior predictive assessment. We illustrate the proposed approach with a simulation study and an empirical application.
GND Keywords: ;
Bayes-Modell
Regressionsanalyse
Keywords: ; ; ; ; ; ;
Bayesian estimation
Post-processing
Reduced rank regression
Orthogonal transformation
Model selection
Stiefel manifold
Posterior predictive assessment
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Peer Reviewed:
Yes:
International Distribution:
Yes:
Type:
Article
Activation date:
January 17, 2025
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https://fis.uni-bamberg.de/handle/uniba/105513