Let X1(1 - 1), X2(1 - p2), and X3(1 - p3) be three sets of random variables distributed jointly as a normal distribution. Let [varrho]1.23 and [varrho]1.2 be the multiple correlation coefficients between X1 and (X2, X3) and between X1 and X2, respectively. Invariant tests for the following four...

Let V1,..., Vm, W1,..., Wn be independent p - 1 random vectors having multivariate normal distributions with common nonsingular covariance matrix [Sigma] and with EW[alpha] = 0, [alpha] = 1,..., n. In this canonical form of the multivariate linear model, the problem is to test H: EV[alpha] az...