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

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.