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On the distributions of some test criteria for a covariance matrix under local alternatives and bootstrap approximations

Author

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  • Nagao, Hisao
  • Srivastava, M. S.

Abstract

The asymptotic distribution of some test criteria for a covariance matrix are derived under local alternatives. Except for the existence of some higher moments, no assumption as to the form of the distribution function is made. As an illustration, a case of t distribution included normal model is considered and the power of the likelihood ratio test and Nagao's test for sphericity, as described in Srivastava and Khatri and Anderson, is computed. Also, the power is computed using the bootstrap method. In the case of t distribution, the bootstrap approximation does not appear to be as good as the one obtained by the asymptotic expansion method.

Suggested Citation

  • Nagao, Hisao & Srivastava, M. S., 1992. "On the distributions of some test criteria for a covariance matrix under local alternatives and bootstrap approximations," Journal of Multivariate Analysis, Elsevier, vol. 43(2), pages 331-350, November.
    • Handle: RePEc:eee:jmvana:v:43:y:1992:i:2:p:331-350
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    Cited by:

    1. Srivastava, Muni S. & Kollo, Tõnu & von Rosen, Dietrich, 2011. "Some tests for the covariance matrix with fewer observations than the dimension under non-normality," Journal of Multivariate Analysis, Elsevier, vol. 102(6), pages 1090-1103, July.
    2. Yanagihara, Hirokazu & Tonda, Tetsuji & Matsumoto, Chieko, 2005. "The effects of nonnormality on asymptotic distributions of some likelihood ratio criteria for testing covariance structures under normal assumption," Journal of Multivariate Analysis, Elsevier, vol. 96(2), pages 237-264, October.
    3. Marc Hallin, 2008. "On the Non Gaussian Asymptotics of the Likelihood Ratio Test Statistic for Homogeneity of Covariance," Working Papers ECARES 2008_039, ULB -- Universite Libre de Bruxelles.

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