Asymptotic expansions for the distributions of some functions of the latent roots of matrices in three situations

In this paper we derive asymptotic expansions for the distributions of some functions of the latent roots of the matrices in three situations in multivariate normal theory, i.e., (i) principal component analysis, (ii) MANOVA model and (iii) canonical correlation analysis. These expansions are obtained by using a perturbation method. Confidence intervals for the functions of the corresponding population roots are also obtained.