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Covariance reducing models: An alternative to spectral modelling of covariance matrices

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  • R. Dennis Cook
  • Liliana Forzani

Abstract

We introduce covariance reducing models for studying the sample covariance matrices of a random vector observed in different populations. The models are based on reducing the sample covariance matrices to an informational core that is sufficient to characterize the variance heterogeneity among the populations. They possess useful equivariance properties and provide a clear alternative to spectral models for covariance matrices. Copyright 2008, Oxford University Press.

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  • R. Dennis Cook & Liliana Forzani, 2008. "Covariance reducing models: An alternative to spectral modelling of covariance matrices," Biometrika, Biometrika Trust, vol. 95(4), pages 799-812.
    • Handle: RePEc:oup:biomet:v:95:y:2008:i:4:p:799-812
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    File URL: http://hdl.handle.net/10.1093/biomet/asn052
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    Cited by:

    1. Forzani, Liliana & Rodriguez, Daniela & Smucler, Ezequiel & Sued, Mariela, 2019. "Sufficient dimension reduction and prediction in regression: Asymptotic results," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 339-349.
    2. Velilla, Santiago, 2010. "On the structure of the quadratic subspace in discriminant analysis," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1239-1251, May.
    3. Adragni, Kofi Placid & Cook, R. Dennis & Wu, Seongho, 2012. "GrassmannOptim: An R Package for Grassmann Manifold Optimization," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 50(i05).
    4. Alexander M. Franks, 2022. "Reducing subspace models for large‐scale covariance regression," Biometrics, The International Biometric Society, vol. 78(4), pages 1604-1613, December.
    5. Schott, James R., 2012. "A note on maximum likelihood estimation for covariance reducing models," Statistics & Probability Letters, Elsevier, vol. 82(9), pages 1629-1631.
    6. Pan, Yuqing & Mai, Qing, 2020. "Efficient computation for differential network analysis with applications to quadratic discriminant analysis," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).

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