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

Dorota Kurowicka

Journal of Multivariate Analysis, 2014, vol. 129, issue C, 160-170

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.

Keywords: Distribution of correlation matrix; Sampling correlation matrix; Volume measure of partially specified correlation matrix (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.jmva.2014.04.006

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