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Asymptotic optimality of multivariate linear hypothesis tests

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  • Baringhaus, Ludwig

Abstract

The optimal exponential rate at which the Type II error probability of a multivariate linear hypothesis test can tend to zero while the Type I error probability is held fixed is given. The likelihood ratio test, the test of Hotelling and Lawley, the test of Bartlett, Nanda, and Pillai, and the test of Roy are shown to be asymptotically optimal in the sense that for each of these tests the exponential rate of convergence of the type II error probability attains the optimal value. Some other tests for the multivariate linear hypothesis are shown not to be asymptotically optimal.

Suggested Citation

  • Baringhaus, Ludwig, 1987. "Asymptotic optimality of multivariate linear hypothesis tests," Journal of Multivariate Analysis, Elsevier, vol. 23(2), pages 303-311, December.
    • Handle: RePEc:eee:jmvana:v:23:y:1987:i:2:p:303-311
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    Cited by:

    1. Baringhaus, Ludwig & Gaigall, Daniel, 2017. "Hotelling’s T2 tests in paired and independent survey samples: An efficiency comparison," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 177-198.

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