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MANOVA in the multivariate components of variance model

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  • Mathew, Thomas

Abstract

Conditions are obtained for the multivariate components of variance model to admit a multivariate analysis of variance (MANOVA). MANOVA in this setup is defined as a partition of the sum of squares and sum of products matrix into independent Wishart matrices. A minimal sufficient statistic is exhibited using the terms in the MANOVA and its completeness is discussed. The results are illustrated using examples.

Suggested Citation

  • Mathew, Thomas, 1989. "MANOVA in the multivariate components of variance model," Journal of Multivariate Analysis, Elsevier, vol. 29(1), pages 30-38, April.
    • Handle: RePEc:eee:jmvana:v:29:y:1989:i:1:p:30-38
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    Citations

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    Cited by:

    1. Mathew, Thomas & Nordström, Kenneth, 1997. "Wishart and Chi-Square Distributions Associated with Matrix Quadratic Forms," Journal of Multivariate Analysis, Elsevier, vol. 61(1), pages 129-143, April.
    2. Mortarino, Cinzia, 2005. "A decomposition for a stochastic matrix with an application to MANOVA," Journal of Multivariate Analysis, Elsevier, vol. 92(1), pages 134-144, January.
    3. Speed, Terence P. & Hicks, Damien G., 2022. "Spectral PCA for MANOVA and data over binary trees," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    4. Gupta, Arjun K. & Harrar, Solomon W. & Fujikoshi, Yasunori, 2006. "Asymptotics for testing hypothesis in some multivariate variance components model under non-normality," Journal of Multivariate Analysis, Elsevier, vol. 97(1), pages 148-178, January.
    5. Hu, Jianhua, 2008. "Wishartness and independence of matrix quadratic forms in a normal random matrix," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 555-571, March.
    6. Kim, Chulmin & Zimmerman, Dale L., 2012. "Unconstrained models for the covariance structure of multivariate longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 104-118.
    7. Stavytskyy Andriy & Prokopenko Oleksandra, 2017. "Investments in Agricultural Machinery and Its Efficiency in Ukraine," Ekonomika (Economics), Sciendo, vol. 96(1), pages 113-130, January.
    8. Masaro, Joe & Wong, Chi Song, 2010. "Wishart-Laplace distributions associated with matrix quadratic forms," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1168-1178, May.

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