Moments and distributions of certain multivariate test criteria in the canonical correlation case under violation

摘要: Abstract The joint probability density function (pdf) and the moments of order h general multivariate statistic defined by Y (p) (a,b) = П p i 1 l a (1 - ) b , where are positive real numbers, obtained in this paper canonical correlation case expressed terms H-function. Alternative forms some test criteria also furnished Meijer G-function. Explicit pdf cdf supplemented 2. Here l1, l2, …, lp latent roots matrix L λR(1 + λR)−1, R S1S−12, λ > 0. covariance matrices S1 S2 independently distributed have, respectively, noncentral Wishart distribution W( p, n Σ Щ) Щ 2 MM′Σ −1 central W(p, n2, Σ2, 0). derivation is based on Pillai's S1S−12 under violation. It necessary to point out that violation means assumption normality violated common disturbed. Furthermore, such as, Wilks, Wilks-Lawely modified likelihood ratio may be deduced from results associated with as special cases. used further investigate exact robustness against nonnormality independence.