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Tests for Multivariate Analysis of Variance in High Dimension Under Non-Normality

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  • Muni S. Srivastava

    (Department of Statistics, University of Toronto)

  • Tatsuya Kubokawa

    (Faculty of Economics, University of Tokyo)

Abstract

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.

Suggested Citation

  • Muni S. Srivastava & Tatsuya Kubokawa, 2011. "Tests for Multivariate Analysis of Variance in High Dimension Under Non-Normality," CIRJE F-Series CIRJE-F-831, CIRJE, Faculty of Economics, University of Tokyo.
  • Handle: RePEc:tky:fseres:2011cf831
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    File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2011/2011cf831.pdf
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    1. Schott, James R., 2007. "Some high-dimensional tests for a one-way MANOVA," Journal of Multivariate Analysis, Elsevier, vol. 98(9), pages 1825-1839, October.
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