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Spectral models for covariance matrices

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  • Robert J. Boik
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    Abstract

    A new model for the simultaneous eigenstructure of multiple covariance matrices is proposed. The model is much more flexible than existing models and subsumes most of them as special cases. A Fisher scoring algorithm for computing maximum likelihood estimates of the parameters under normality is given. Asymptotic distributions of the estimators are derived under normality as well as under arbitrary distributions having finite fourth-order cumulants. Special attention is given to elliptically contoured distributions. Likelihood ratio tests are described and sufficient conditions are given under which the test statistics are asymptotically distributed as chi-squared random variables. Procedures are derived for evaluating Bartlett corrections under normality. Some conjectures made by Flury (1988) are verified; others are refuted. A small simulation study of the adequacy of the Bartlett correction is described and the new procedures are illustrated on two datasets. Copyright Biometrika Trust 2002, Oxford University Press.

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    Bibliographic Info

    Article provided by Biometrika Trust in its journal Biometrika.

    Volume (Year): 89 (2002)
    Issue (Month): 1 (March)
    Pages: 159-182

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    Handle: RePEc:oup:biomet:v:89:y:2002:i:1:p:159-182

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    Cited by:
    1. Boik, Robert J., 2005. "Second-order accurate inference on eigenvalues of covariance and correlation matrices," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 136-171, September.
    2. Pourahmadi, Mohsen & Daniels, Michael J. & Park, Trevor, 2007. "Simultaneous modelling of the Cholesky decomposition of several covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 98(3), pages 568-587, March.
    3. Daniels, Michael J., 2006. "Bayesian modeling of several covariance matrices and some results on propriety of the posterior for linear regression with correlated and/or heterogeneous errors," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1185-1207, May.
    4. Marc Hallin & Davy Paindaveine & Thomas Verdebout, 2011. "Optimal Rank-Based Tests for Common Principal Components," Working Papers ECARES ECARES 2011-032, ULB -- Universite Libre de Bruxelles.
    5. Boik, Robert J., 2013. "Model-based principal components of correlation matrices," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 310-331.

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