CIRJE-F-831 "Tests for Multivariate Analysis of Variance in High Dimension Under Non-Normality"
Author Name Srivastava, Muni S. and Tatsuya Kubokawa
Date December 2011
Full Paper   PDF file
Remarks  Revised in January 2011; subsequetnly published in Journal of Multivariate Analysis, 115, Issue 1, 204-216, 2013

In this article, we consider the problem of testing the equality of mean vectors of dimension ρ 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 ρ. 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[7], Srivastava [5] and Schott[3]. All these tests are not invariant under the change of units of measurements. On the lines of Srivastava and Du[8] and Srivastava[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, ρ) → ∞ and N may be less than ρ and the observation vectors follow a general non-normal model.