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Comparison of powers of a class of tests for multivariate linear hypothesis and independence

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  • Fujikoshi, Yasunori

Abstract

In this paper we consider the class C of test statistics T = [Sigma]j = 1p Q(lj) for testing the multivarite linear hypothesis and independence of two sets of variables. Here Q(l) is a monotone increasing function for l >= 0, Q(0) = 0, Q'(0) = 1, and has a continuous third order derivative in a neighborhood of l = 0. This class includes the likelihood ratio test, Lawley-Hotelling trace test and Bartlett-Nanda-Pillai trace test. We compare the local powers of tests on the basis of the asymptotic expansions of their distributions. The differences in the powers of all the test in C can be explained in terms of [gamma] = Q''(0). The comparisons reveal no uniform superiority properties.

Suggested Citation

  • Fujikoshi, Yasunori, 1988. "Comparison of powers of a class of tests for multivariate linear hypothesis and independence," Journal of Multivariate Analysis, Elsevier, vol. 26(1), pages 48-58, July.
    • Handle: RePEc:eee:jmvana:v:26:y:1988:i:1:p:48-58
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    Citations

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    Cited by:

    1. Kakizawa, Yoshihide & Iwashita, Toshiya, 2008. "A comparison of higher-order local powers of a class of one-way MANOVA tests under general distributions," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1128-1153, July.
    2. Siotani, Minoru & Wakaki, Hirofumi, 2006. "Contributions to multivariate analysis by Professor Yasunori Fujikoshi," Journal of Multivariate Analysis, Elsevier, vol. 97(9), pages 1914-1926, October.
    3. Kakizawa, Yoshihide, 2009. "Third-order power comparisons for a class of tests for multivariate linear hypothesis under general distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 473-496, March.

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