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Likelihood Ratio Tests for Covariance Structure in Random Effects Models

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  • Kuriki, S.

Abstract

Let W be a p - p matrix distributed according to the Wishart distribution Wp(n, [Phi]) with [Phi] positive definite and n >= p. Let ([nu]n/[sigma]2) g be distributed according to the chi-squared distribution [chi]2([nu]n). Consider hierarchical hypotheses H0 [subset of] H1 [subset of] H2 that H0: [Phi] = [sigma]2Ip, H1: [Phi] >= [sigma]2Ip, and H2: [Phi], [sigma]2 are unrestricted. The unbiasedness of the likelihood ratio test (LRT) for testing H0 against H1 - H0 is proved. The LRT for H1 against H2 - H1 is shown to have monotonic property of its power function but not unbiased. As n goes to infinity, limiting null distributions of these two LRT statistics are obtained as mixtures of chi-squared distributions. For a general class of tests for H0 against H1 - H0 including LRT, the local unbiasedness is proved using FKG inequality. Here a new sufficient condition for the FKG condition is posed. These LRTs are shown to have applications to the random effects models introduced by C. R. Rao (1965, Biometrika52, 447-458).

Suggested Citation

  • Kuriki, S., 1993. "Likelihood Ratio Tests for Covariance Structure in Random Effects Models," Journal of Multivariate Analysis, Elsevier, vol. 46(2), pages 175-197, August.
    • Handle: RePEc:eee:jmvana:v:46:y:1993:i:2:p:175-197
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    Cited by:

    1. Lutz Dümbgen, 1995. "Minimax tests for convex cones," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(1), pages 155-165, January.

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