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A note on the power superiority of the restricted likelihood ratio test

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  • Praestgaard, Jens

Abstract

Let be a closed convex cone which contains a linear subspace . We investigate the restricted likelihood ratio test for the null and alternative hypotheses based on an n-dimensional, normally distributed random vector (X1,...,Xn) with unknown mean and known covariance matrix [Sigma]. We prove that if the true mean vector satisfies the alternative hypothesis HA, then the restricted likelihood ratio test is more powerful than the unrestricted test with larger alternative hypothesis [real]n. The proof uses isoperimetric inequalities for the uniform distribution on the n-dimensional sphere and for n-dimensional standard Gaussian measure.

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  • Praestgaard, Jens, 2012. "A note on the power superiority of the restricted likelihood ratio test," Journal of Multivariate Analysis, Elsevier, vol. 104(1), pages 1-15, February.
    • Handle: RePEc:eee:jmvana:v:104:y:2012:i:1:p:1-15
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    References listed on IDEAS

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    1. Cohen, Arthur & Kemperman, J. H. B. & Sackrowitz, Harold B., 2000. "Properties of Likelihood Inference for Order Restricted Models," Journal of Multivariate Analysis, Elsevier, vol. 72(1), pages 50-77, January.
    2. Tsai, Mingtan, 1992. "On the power superiority of likelihood ratio tests for restricted alternatives," Journal of Multivariate Analysis, Elsevier, vol. 42(1), pages 102-109, July.
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