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Some high-dimensional tests for a one-way MANOVA

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  • Schott, James R.
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    Abstract

    A statistic is proposed for testing the equality of the mean vectors in a one-way multivariate analysis of variance. The asymptotic null distribution of this statistic, as both the sample size and the number of variables go to infinity, is shown to be normal. Thus, this test can be used when the number of variables is not small relative to the sample size. In particular, it can be used when the number of variables exceeds the degrees of freedom for error, a situation in which standard MANOVA tests are invalid. A related statistic, also having an asymptotic normal distribution, is developed for tests concerning the dimensionality of the hyperplane formed by the population mean vectors. The finite sample size performances of the normal approximations are evaluated in a simulation study.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 98 (2007)
    Issue (Month): 9 (October)
    Pages: 1825-1839

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    Handle: RePEc:eee:jmvana:v:98:y:2007:i:9:p:1825-1839

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    Related research

    Keywords: High-dimensional data Testing the equality of mean vectors Tests of dimensionality;

    References

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    1. Schott, James R., 2006. "A high-dimensional test for the equality of the smallest eigenvalues of a covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 97(4), pages 827-843, April.
    2. 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.
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    Cited by:
    1. Schott, James R., 2007. "A test for the equality of covariance matrices when the dimension is large relative to the sample sizes," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6535-6542, August.
    2. J. Cuesta-Albertos & M. Febrero-Bande, 2010. "A simple multiway ANOVA for functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 19(3), pages 537-557, November.

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