In the univariate case it is well known that the one sided t test is uniformly most powerful for the null hypothesis against all one sided alternatives. Such a property does not easily extend to the multivariate case. In this paper, a test derived for the hypothesis that the mean of a vector...

The paper extends the results of Khatri to complex elliptical variates. Asymptotic confidence bounds on location parameters for the linear growth curve for the complex variates, the asymptotic distribution of the canonical correlations for the two sets of complex variates, and the asymptotic...

It is established that a vector variable (X1, ..., Xk) has a multivariate normal distribution if for each Xi the regression on the rest is linear and the conditional distribution about the regression does not depend on the rest of the variables, provided the regression coefficients satisfy some...

Optimization problems are connected with maximization of three functions, namely, geometric mean, arithmetic mean and harmonic mean of the eigenvalues of (X'[Sigma]X)-1[Sigma]Y(Y'[Sigma]Y)-1Y'[Sigma]X, where [Sigma] is positive definite, X and Y are p - r and p - s matrices of ranks r and s...

Let x have a spherical distribution (SD), with characteristic function [phi](t't), t [epsilon] Tp, to be denoted by x [approximate] Sp([phi]). Let x'Ax be a quadratic form, with A = A'. A correction is given to Theorem 1 in Khatri and Mukerjee (1987), wrongly asserting that if Q = x'Ax is...

We derive various results for the uniform distribution on a Stiefel manifold and propose a test of uniformity.

For the linear growth curve model introduced by Potthoff and Roy (Biometrika 51 (1964), 313-326), various likelihood ratio tests and some ad hoc tests are available for the location and scale parameters on the basis of normally distributed error components. We study these tests under the...