A test statistic for the equality of g 2 mean vectors, with particularemphasis on the MANOVA case for g 3, is derived when the dimensionp of the vectors may exceed the number of such vectors, ni, i = 1; : : : ; g.The asymptotic distribution of the test statistic, composed of linear com-binations of one- and two-sample U-statistics with degenerate bivariatekernels, is derived under fairly general conditions. In particular, the g pop-ulations do not need to be necessarily normal and may also have unequalcovariance matrices. Under certain mild assumptions on the moments ofthe eigenvalues of unknown covariance matrices, the limit distribution ofthe test statistic is shown to follow a 2 distribution, further extended tonormal limit, as ni; p ! 1. The statistic is further extended for testingany general linear hypothesis, taking prole analysis as one of the mostcommonly used cases. Extensive simulation results are used to show theaccuracy of the test statistic for both test size and power. Practical useof the test statistics is also demonstrated using real data examples.
2014. , 12 p.