A high-dimensional test for the equality of the smallest eigenvalues of a covariance matrix
Journal of Multivariate Analysis
Multivariate analysis of variance with fewer observations than the dimension
Journal of Multivariate Analysis - Special issue dedicated to Professor Yasunori Fujikoshi
Computational Statistics & Data Analysis
Tests for multivariate analysis of variance in high dimension under non-normality
Journal of Multivariate Analysis
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A statistic is proposed for testing the equality of the mean vectors in a one-way multivariate analysis of variance. The asymptotic null distribution of this statistic, as both the sample size and the number of variables go to infinity, is shown to be normal. Thus, this test can be used when the number of variables is not small relative to the sample size. In particular, it can be used when the number of variables exceeds the degrees of freedom for error, a situation in which standard MANOVA tests are invalid. A related statistic, also having an asymptotic normal distribution, is developed for tests concerning the dimensionality of the hyperplane formed by the population mean vectors. The finite sample size performances of the normal approximations are evaluated in a simulation study.