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Testing 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. These LCI models have especially tractable statistical properties and arise naturally in the analysis of non-monotone multivariate missing data patterns and non-nested dependent linear regression models [reverse not equivalent] seemingly unrelated regressions. The present paper treats the problem of testing one LCI model against another, i.e., testing N() vs N() when is a subring of . The likelihood ratio test statistic is derived, together with its central distribution, and several examples are presented.

Suggested Citation

  • Andersson, S. A. & Perlman, M. D., 1995. "Testing Lattice Conditional Independence Models," Journal of Multivariate Analysis, Elsevier, vol. 53(1), pages 18-38, April.
    • Handle: RePEc:eee:jmvana:v:53:y:1995:i:1:p:18-38
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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. Drton, Mathias & Andersson, Steen A. & Perlman, Michael D., 2006. "Conditional independence models for seemingly unrelated regressions with incomplete data," Journal of Multivariate Analysis, Elsevier, vol. 97(2), pages 385-411, February.
    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. Wu, Lang & Perlman, Michael D., 2000. "Testing lattice conditional independence models based on monotone missing data," Statistics & Probability Letters, Elsevier, vol. 50(2), pages 193-201, November.
    5. 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.

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