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.
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