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Joint density of correlations in the correlation matrix with chordal sparsity patterns

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  • Kurowicka, Dorota

Abstract

We extend the methodology of generating the random correlation matrix of Joe (2006) and Lewandowski et al. (2009) by introducing a partial correlation expansion of the determinant of a correlation matrix which is more general than the partial correlations on a regular vine used in Lewandowski et al. (2009). This generalization allows us to formulate the partial correlation expansion of determinant for a correlation matrix with a chordal sparsity pattern. For such a partially specified correlation matrix we find a uniform density of unspecified correlations. This leads to a closed form formula for the volume of the space of correlation matrices with specified correlations corresponding to a chordal graph. We present an algorithm to generate uniformly a random correlation matrix with a chordal sparsity pattern.

Suggested Citation

  • Kurowicka, Dorota, 2014. "Joint density of correlations in the correlation matrix with chordal sparsity patterns," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 160-170.
    • Handle: RePEc:eee:jmvana:v:129:y:2014:i:c:p:160-170
    DOI: 10.1016/j.jmva.2014.04.006
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    References listed on IDEAS

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    1. Lewandowski, Daniel & Kurowicka, Dorota & Joe, Harry, 2009. "Generating random correlation matrices based on vines and extended onion method," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 1989-2001, October.
    2. Joe, Harry, 2006. "Generating random correlation matrices based on partial correlations," Journal of Multivariate Analysis, Elsevier, vol. 97(10), pages 2177-2189, November.
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    Cited by:

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    2. Forrester, Peter J. & Zhang, Jiyuan, 2020. "Parametrising correlation matrices," Journal of Multivariate Analysis, Elsevier, vol. 178(C).

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