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Asymptotic expansions of the distributions of the latent roots and the latent vector of the Wishart and multivariate F matrices |
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| Authors: | Nariaki Sugiura |
| Institution: | Department of Information and Behavioral Science, Hiroshima University, Hiroshima, Japan |
| Abstract: | Asymptotic expansions of the joint distributions of the latent roots of the Wishart matrix and multivariate F matrix are obtained for large degrees of freedom when the population latent roots have arbitrary multiplicity. Asymptotic expansions of the distributions of the latent vectors of the above matrices are also derived when the corresponding population root is simple. The effect of normalizations of the vector is examined. |
| Keywords: | Asymptotic expansions Distributions of latent roots Distributions of a latent vector Wishart distribution Multiple population latent roots Perturbation Taylor series expansion for latent root Taylor series expansion for latent vector Effect of normalizations of the latent vector |
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