MCMC Estimation of Restricted Covariance Matrices

Chan, Joshua Chi-Chun and Jeliazkov, Ivan (2009) MCMC Estimation of Restricted Covariance Matrices. Journal of Computational and Graphical Statistics, 18 2: 457-480. doi:10.1198/jcgs.2009.08095

Author Chan, Joshua Chi-Chun
Jeliazkov, Ivan
Title MCMC Estimation of Restricted Covariance Matrices
Journal name Journal of Computational and Graphical Statistics   Check publisher's open access policy
ISSN 1061-8600
Publication date 2009-06-01
Sub-type Article (original research)
DOI 10.1198/jcgs.2009.08095
Volume 18
Issue 2
Start page 457
End page 480
Total pages 24
Editor David Van Dyk
Place of publication United States
Publisher American Statistical Association
Collection year 2010
Language eng
Subject C1
970101 Expanding Knowledge in the Mathematical Sciences
010401 Applied Statistics
Abstract This article is motivated by the difficulty of applying standard simulation techniques when identification constraints or theoretical considerations induce covariance restrictions in multivariate models. To deal with this difficulty, we build upon a decomposition of positive definite matrices and show that it leads to straightforward Markov chain Monte Carlo samplers for restricted covariance matrices. We introduce the approach by reviewing results for multivariate Gaussian models without restrictions, where standard conjugate priors on the elements of the decomposition induce the usual Wishart distribution on the precision matrix and vice versa. The unrestricted case provides guidance for constructing efficient Metropolis–Hastings and accept-reject Metropolis–Hastings samplers in more complex settings, and we describe in detail how simulation can be performed under several important constraints. The proposed approach is illustrated in a simulation study and two applications in economics. Supplemental materials for this article (appendixes, data, and computer code) are available online.
Q-Index Code C1
Q-Index Status Confirmed Code

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
2010 Higher Education Research Data Collection
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Citation counts: TR Web of Science Citation Count  Cited 5 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 4 times in Scopus Article | Citations
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Created: Wed, 24 Mar 2010, 13:15:50 EST by Kay Mackie on behalf of School of Mathematics & Physics