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Asymptotic expansions of the distributions of the latent roots in MANOVA and the canonical correlations

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  • Fujikoshi, Y.

Abstract

Asymptotic expansions are given for the density function of the normalized latent roots of S1S2-1 for large n under the assumption of [Omega] = O(n), where S1 and S2 are independent noncentral and central Wishart matrices having the Wp(b, [Sigma]; [Omega]) and Wp(n, [Sigma]) distributions, respectively. The expansions are obtained by using a perturbation method. Asymptotic expansions are also obtained for the density function of the normalized canonical correlations when some of the population canonical correlations are zero.

Suggested Citation

  • Fujikoshi, Y., 1977. "Asymptotic expansions of the distributions of the latent roots in MANOVA and the canonical correlations," Journal of Multivariate Analysis, Elsevier, vol. 7(3), pages 386-396, September.
    • Handle: RePEc:eee:jmvana:v:7:y:1977:i:3:p:386-396
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    Cited by:

    1. 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.

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