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The likelihood ratio tests for the dimensionality of regression coefficients

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  • Fujikoshi, Yasunori

Abstract

In this paper we give a unified derivation of the likelihood ratio (LR) statistics for testing the hypothesis on the dimensionality of regression coefficients under a usual MANOVA model. We also derive the LR statistics under a general MANOVA model and study their asymptotic null and nonnull distributions. Further it is shown that the test statistic used by Bartlett [4] for testing the hypothesis that the last p-k canonical correlations are all zero is the LR statistic.

Suggested Citation

  • Fujikoshi, Yasunori, 1974. "The likelihood ratio tests for the dimensionality of regression coefficients," Journal of Multivariate Analysis, Elsevier, vol. 4(3), pages 327-340, September.
    • Handle: RePEc:eee:jmvana:v:4:y:1974:i:3:p:327-340
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    Cited by:

    1. Gonzalo Camba-Mendez & George Kapetanios, 2005. "Statistical Tests of the Rank of a Matrix and Their Applications in Econometric Modelling," Working Papers 541, Queen Mary University of London, School of Economics and Finance.
    2. Siotani, Minoru & Wakaki, Hirofumi, 2006. "Contributions to multivariate analysis by Professor Yasunori Fujikoshi," Journal of Multivariate Analysis, Elsevier, vol. 97(9), pages 1914-1926, October.
    3. Calinski, Tadeusz & Lejeune, Michel, 1998. "Dimensionality in Manova Tested by a Closed Testing Procedure," Journal of Multivariate Analysis, Elsevier, vol. 65(2), pages 181-194, May.
    4. Boik, Robert J., 1998. "A Local Parameterization of Orthogonal and Semi-Orthogonal Matrices with Applications," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 244-276, November.

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