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Generating random correlation matrices based on partial correlations

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  • Joe, Harry
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    Abstract

    A d-dimensional positive definite correlation matrix R=([rho]ij) can be parametrized in terms of the correlations [rho]i,i+1 for i=1,...,d-1, and the partial correlations [rho]iji+1,...j-1 for j-i[greater-or-equal, slanted]2. These parameters can independently take values in the interval (-1,1). Hence we can generate a random positive definite correlation matrix by choosing independent distributions Fij, 1[less-than-or-equals, slant]i

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 97 (2006)
    Issue (Month): 10 (November)
    Pages: 2177-2189

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    Handle: RePEc:eee:jmvana:v:97:y:2006:i:10:p:2177-2189

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    Keywords: Beta distribution Determinant of correlation matrix;

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    Cited by:
    1. Daniels, M.J. & Pourahmadi, M., 2009. "Modeling covariance matrices via partial autocorrelations," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 100(10), pages 2352-2363, November.
    2. Joseph Romano & Azeem Shaikh & Michael Wolf, 2008. "Control of the false discovery rate under dependence using the bootstrap and subsampling," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, Springer, vol. 17(3), pages 417-442, November.
    3. Kirschstein, Thomas & Liebscher, Steffen & Becker, Claudia, 2013. "Robust estimation of location and scatter by pruning the minimum spanning tree," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 120(C), pages 173-184.
    4. Lewandowski, Daniel & Kurowicka, Dorota & Joe, Harry, 2009. "Generating random correlation matrices based on vines and extended onion method," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 100(9), pages 1989-2001, October.
    5. Böhm, Walter & Hornik, Kurt, 2014. "Generating random correlation matrices by the simple rejection method: Why it does not work," Statistics & Probability Letters, Elsevier, Elsevier, vol. 87(C), pages 27-30.
    6. Christopher J. Bennett, 2009. "p-Value Adjustments for Asymptotic Control of the Generalized Familywise Error Rate," Vanderbilt University Department of Economics Working Papers 0905, Vanderbilt University Department of Economics.
    7. Wang, Y. & Daniels, M.J., 2013. "Bayesian modeling of the dependence in longitudinal data via partial autocorrelations and marginal variances," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 116(C), pages 130-140.

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