Tests for multivariate analysis of variance in high dimension under non-normality

In this article, we consider the problem of testing the equality of mean vectors of dimension p of several groups with a common unknown non-singular covariance matrix Σ , based on N independent observation vectors where N may be less than the dimension p . This problem, known in the literature as the multivariate analysis of variance (MANOVA) in high-dimension has recently been considered in the statistical literature by Srivastava and Fujikoshi (2006) [8], Srivastava (2007) [5] and Schott (2007) [3]. All these tests are not invariant under the change of units of measurements. On the lines of Srivastava and Du (2008) [7] and Srivastava (2009) [6], we propose a test that has the above invariance property. The null and the non-null distributions are derived under the assumption that ( N , p ) → ∞ and N may be less than p and the observation vectors follow a general non-normal model.