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Distribution of random correlation matrices: Hyperspherical parameterization of the Cholesky factor

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  • Pourahmadi, Mohsen
  • Wang, Xiao

Abstract

We study the distribution of random correlation matrices using the hyperspherical parameterization of their Cholesky factors and the distributions of the related angles. We highlight the roles of this procedure in generating high-dimensional correlation matrices.

Suggested Citation

  • Pourahmadi, Mohsen & Wang, Xiao, 2015. "Distribution of random correlation matrices: Hyperspherical parameterization of the Cholesky factor," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 5-12.
    • Handle: RePEc:eee:stapro:v:106:y:2015:i:c:p:5-12
    DOI: 10.1016/j.spl.2015.06.015
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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. Madar, Vered, 2015. "Direct formulation to Cholesky decomposition of a general nonsingular correlation matrix," Statistics & Probability Letters, Elsevier, vol. 103(C), pages 142-147.
    3. Joe, Harry, 2006. "Generating random correlation matrices based on partial correlations," Journal of Multivariate Analysis, Elsevier, vol. 97(10), pages 2177-2189, November.
    4. Weiping Zhang & Chenlei Leng & Cheng Yong Tang, 2015. "A joint modelling approach for longitudinal studies," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(1), pages 219-238, January.
    5. Frederick Wong, 2003. "Efficient estimation of covariance selection models," Biometrika, Biometrika Trust, vol. 90(4), pages 809-830, December.
    6. Kawee Numpacharoen & Amporn Atsawarungruangkit, 2012. "Generating Correlation Matrices Based on the Boundaries of Their Coefficients," PLOS ONE, Public Library of Science, vol. 7(11), pages 1-7, November.
    7. Böhm, Walter & Hornik, Kurt, 2014. "Generating random correlation matrices by the simple rejection method: Why it does not work," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 27-30.
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    Cited by:

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    11. Riccardo Lucchetti & Luca Pedini, 2025. "Correction to: The Spherical Parametrisation for Correlation Matrices and its Computational Advantages," Computational Economics, Springer;Society for Computational Economics, vol. 65(4), pages 2449-2450, April.

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