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Simultaneous modelling of the Cholesky decomposition of several covariance matrices

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  • Pourahmadi, Mohsen
  • Daniels, Michael J.
  • Park, Trevor
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    Abstract

    A method for simultaneous modelling of the Cholesky decomposition of several covariance matrices is presented. We highlight the conceptual and computational advantages of the unconstrained parameterization of the Cholesky decomposition and compare the results with those obtained using the classical spectral (eigenvalue) and variance-correlation decompositions. All these methods amount to decomposing complicated covariance matrices into "dependence" and "variance" components, and then modelling them virtually separately using regression techniques. The entries of the "dependence" component of the Cholesky decomposition have the unique advantage of being unconstrained so that further reduction of the dimension of its parameter space is fairly simple. Normal theory maximum likelihood estimates for complete and incomplete data are presented using iterative methods such as the EM (Expectation-Maximization) algorithm and their improvements. These procedures are illustrated using a dataset from a growth hormone longitudinal clinical trial.

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    Bibliographic Info

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

    Volume (Year): 98 (2007)
    Issue (Month): 3 (March)
    Pages: 568-587

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    Handle: RePEc:eee:jmvana:v:98:y:2007:i:3:p:568-587

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    Related research

    Keywords: Common principal components Longitudinal data Maximum likelihood estimation Missing data Spectral decomposition Variance-correlation decomposition;

    References

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    1. Fraley C. & Raftery A.E., 2002. "Model-Based Clustering, Discriminant Analysis, and Density Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 611-631, June.
    2. Robert J. Boik, 2002. "Spectral models for covariance matrices," Biometrika, Biometrika Trust, vol. 89(1), pages 159-182, March.
    3. Robert J. Boik, 2003. "Principal component models for correlation matrices," Biometrika, Biometrika Trust, vol. 90(3), pages 679-701, September.
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    Cited by:
    1. Fisher, Thomas J. & Sun, Xiaoqian, 2011. "Improved Stein-type shrinkage estimators for the high-dimensional multivariate normal covariance matrix," Computational Statistics & Data Analysis, Elsevier, vol. 55(5), pages 1909-1918, May.

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