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

Author

Listed:
  • 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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    References listed on IDEAS

    as
    1. Srivastava, Muni S., 2009. "A test for the mean vector with fewer observations than the dimension under non-normality," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 518-532, March.
    2. 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.
    3. Srivastava, Muni S. & Fujikoshi, Yasunori, 2006. "Multivariate analysis of variance with fewer observations than the dimension," Journal of Multivariate Analysis, Elsevier, vol. 97(9), pages 1927-1940, October.
    4. Srivastava, Muni S. & Du, Meng, 2008. "A test for the mean vector with fewer observations than the dimension," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 386-402, March.
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