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Generating random correlation matrices by the simple rejection method: Why it does not work

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  • Böhm, Walter
  • Hornik, Kurt

Abstract

We derive exact and asymptotic formulas for the probability that a symmetric n×n matrix with unit diagonal and upper diagonal elements i.i.d. uniform on (−1,1) is positive definite (and thus a “random correlation matrix”): this is almost never the case for n≥6.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:87:y:2014:i:c:p:27-30
    DOI: 10.1016/j.spl.2013.12.012
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    References listed on IDEAS

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    1. Joe, Harry, 2006. "Generating random correlation matrices based on partial correlations," Journal of Multivariate Analysis, Elsevier, vol. 97(10), pages 2177-2189, November.
    2. 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.
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    Cited by:

    1. Madar, Vered, 2015. "Direct formulation to Cholesky decomposition of a general nonsingular correlation matrix," Statistics & Probability Letters, Elsevier, vol. 103(C), pages 142-147.
    2. 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.

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