Asymptotic joint distribution of the largest roots of several multivariate F matrices I. Quasi-independent case

An asymptotic expansion of the joint distribution of k largest characteristic roots CM(i)(SiS0-1), i = 1,..., k, is given, where S'is and S0 are independent Wishart matrices with common covariance matrix [Sigma]. The modified second-approximation procedure to the upper percentage points of the maximum of CM(i)(SiS0-1), i = 1,..., k, is also considered. The evaluation of the expansion is based on the idea for studentization due to Welch and James with the use of differential operators and of the perturbation procedure.