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Unbiasedness of the Likelihood Ratio Test for Lattice Conditional Independence Models

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  • Andersson, S. A.
  • Perlman, M. D.

Abstract

The lattice conditional independence (LCI) model N() is defined to be the set of all normal distributions N(0, [Sigma]) on I such that for every pair L, M [set membership, variant] , xL and xM are conditionally independent given xL [intersection] M. Here is a ring of subsets (hence a distributive lattice) of the finite index set I such that [empty set][combining character] I [set membership, variant] , while for K [set membership, variant] , xK is the coordinate projection of x [set membership, variant] I onto K. Andersson and Perlman in the preceding paper derived the likelihood ratio (LR) statistic [lambda] for testing one LCI model against another, i.e., for testing N() vs N() based on a random sample from N(0, [Sigma]), where is a subring of . In the present paper the strict unbiasedness of the LR test is established, and related results regarding the distribution of the maximum likelihood estimator of [Sigma] under the LCI model N() are presented.

Suggested Citation

  • Andersson, S. A. & Perlman, M. D., 1995. "Unbiasedness of the Likelihood Ratio Test for Lattice Conditional Independence Models," Journal of Multivariate Analysis, Elsevier, vol. 53(1), pages 1-17, April.
    • Handle: RePEc:eee:jmvana:v:53:y:1995:i:1:p:1-17
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    Cited by:

    1. Chang, Wan-Ying & Richards, Donald St.P., 2009. "Finite-sample inference with monotone incomplete multivariate normal data, I," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 1883-1899, October.
    2. Andersson, Steen A. & Perlman, Michael D., 1998. "Normal Linear Regression Models With Recursive Graphical Markov Structure," Journal of Multivariate Analysis, Elsevier, vol. 66(2), pages 133-187, August.
    3. Jinfang Wang, 2010. "A universal algebraic approach for conditional independence," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(4), pages 747-773, August.
    4. Hélène Massam & Erhard Neher, 1997. "On Transformations and Determinants of Wishart Variables on Symmetric Cones," Journal of Theoretical Probability, Springer, vol. 10(4), pages 867-902, October.
    5. Konno, Yoshihiko, 2001. "Inadmissibility of the Maximum Likekihood Estimator of Normal Covariance Matrices with the Lattice Conditional Independence," Journal of Multivariate Analysis, Elsevier, vol. 79(1), pages 33-51, October.

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