Asymptotic expansions of the distributions of the latent roots in MANOVA and the canonical correlations |
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Authors: | Y Fujikoshi |
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Institution: | 1. Department of Mathematics and Statistics, C.S.I.R.O., Adelaide, Australia;2. Kobe University, Japan |
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Abstract: | Asymptotic expansions are given for the density function of the normalized latent roots of S1S2?1 for large n under the assumption of , where S1 and S2 are independent noncentral and central Wishart matrices having the and Wp(n, Σ) 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. |
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Keywords: | 62H10 62H20 Asymptotic expansions density functions latent roots in MANOVA model canonical correlations perturbation method |
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