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This paper is concerned with the testing bilateral linear hypothesis on themean matrix in the context of the generalized multivariate analysis of variance(GMANOVA) model when the dimensions of the observed vector may exceed thesample size, the design may become unbalanced, the population may not benormal, or the true covariance matrices may be unequal. The suggested testingmethodology can treat many problems such as the one- and two-way MANOVA tests,the test for parallelism in profile analysis, etc., as specific ones. Wepropose 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-nulldistributions are derived under a general high-dimensional asymptotic frameworkthat allows the dimensionality to arbitrarily exceed the sample size of agroup, thereby establishing consistency for the testing criterion. The accuracyof the proposed test in a finite sample is investigated through simulationsconducted for several high-dimensional scenarios and various underlyingpopulation distributions in combination with different within-group covariancestructures. Finally, the proposed test is applied to a high-dimensional two-wayMANOVA problem for DNA microarray data.

Test for mean matrix in GMANOVA model under heteroscedasticity and non-normality for high-dimensional data