Abstract: This study considers multivariate analysis of variance for normal samples in a high-dimensional medium sample size setting. When the sample dimension is larger than the sample size, the classical likelihood ratio test is not defined, because the likelihood function is unbounded. Based on this unboundedness, we propose a new test called the least favorable direction test. The asymptotic distributions of the test statistic are derived under both nonspiked and spiked covariances. The local asymptotic power function of the test is also given. The results for the asymptotic power function and simulations show that the proposed test is particularly powerful under the spiked covariance.

Key words and phrases: High-dimensional data, least favorable direction test, multivariate analysis of variance, principal component analysis, spiked covariance.