  This paper is concerned with the testing bilateral linear hypothesis on the
mean matrix in the context of the generalized multivariate analysis of variance
(GMANOVA) model when the dimensions of the observed vector may exceed the
sample size, the design may become unbalanced, the population may not be
normal, or the true covariance matrices may be unequal. The suggested testing
methodology can treat many problems such as the one- and two-way MANOVA tests,
the test for parallelism in profile analysis, etc., as specific ones. We
propose a bias-corrected estimator of the Frobenius norm for the mean matrix,
which is a key component of the test statistic. The null and non-null
distributions are derived under a general high-dimensional asymptotic framework
that allows the dimensionality to arbitrarily exceed the sample size of a
group, thereby establishing consistency for the testing criterion. The accuracy
of the proposed test in a finite sample is investigated through simulations
conducted for several high-dimensional scenarios and various underlying
population distributions in combination with different within-group covariance
structures. Finally, the proposed test is applied to a high-dimensional two-way
MANOVA problem for DNA microarray data.
