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A chi-square test for dimensionality with non-Gaussian data

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  • Bai, Z. D.
  • He, Xuming

Abstract

The classical theory for testing the null hypothesis that a set of canonical correlation coefficients is zero leads to a chi-square test under the assumption of multi-normality. The test has been used in the context of dimension reduction. In this paper, we study the limiting distribution of the test statistic without the normality assumption, and obtain a necessary and sufficient condition for the chi-square limiting distribution to hold. Implications of the result are also discussed for the problem of dimension reduction.

Suggested Citation

  • Bai, Z. D. & He, Xuming, 2004. "A chi-square test for dimensionality with non-Gaussian data," Journal of Multivariate Analysis, Elsevier, vol. 88(1), pages 109-117, January.
    • Handle: RePEc:eee:jmvana:v:88:y:2004:i:1:p:109-117
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    References listed on IDEAS

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    1. Eaton, M. L. & Tyler, D., 1994. "The Asymptotic Distribution of Singular-Values with Applications to Canonical Correlations and Correspondence Analysis," Journal of Multivariate Analysis, Elsevier, vol. 50(2), pages 238-264, August.
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    Cited by:

    1. Coudret, R. & Girard, S. & Saracco, J., 2014. "A new sliced inverse regression method for multivariate response," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 285-299.
    2. Nkiet, Guy Martial, 2005. "On estimation of the dimensionality in linear canonical analysis," Statistics & Probability Letters, Elsevier, vol. 75(2), pages 103-112, November.
    3. Ogasawara, Haruhiko, 2007. "Asymptotic expansions of the distributions of estimators in canonical correlation analysis under nonnormality," Journal of Multivariate Analysis, Elsevier, vol. 98(9), pages 1726-1750, October.
    4. Haruhiko Ogasawara, 2009. "Asymptotic expansions in the singular value decomposition for cross covariance and correlation under nonnormality," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(4), pages 995-1017, December.
    5. Bura, E. & Yang, J., 2011. "Dimension estimation in sufficient dimension reduction: A unifying approach," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 130-142, January.

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