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Maximum Likelihood Estimation in Gaussian Chain Graph Models under the Alternative Markov Property

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  • MATHIAS DRTON
  • MICHAEL EICHLER

Abstract

. The Andersson–Madigan–Perlman (AMP) Markov property is a recently proposed alternative Markov property (AMP) for chain graphs. In the case of continuous variables with a joint multivariate Gaussian distribution, it is the AMP rather than the earlier introduced Lauritzen–Wermuth–Frydenberg Markov property that is coherent with data‐generation by natural block‐recursive regressions. In this paper, we show that maximum likelihood estimates in Gaussian AMP chain graph models can be obtained by combining generalized least squares and iterative proportional fitting to an iterative algorithm. In an appendix, we give useful convergence results for iterative partial maximization algorithms that apply in particular to the described algorithm.

Suggested Citation

  • Mathias Drton & Michael Eichler, 2006. "Maximum Likelihood Estimation in Gaussian Chain Graph Models under the Alternative Markov Property," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(2), pages 247-257, June.
    • Handle: RePEc:bla:scjsta:v:33:y:2006:i:2:p:247-257
    DOI: 10.1111/j.1467-9469.2006.00482.x
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    Cited by:

    1. Peña Jose M., 2020. "Unifying Gaussian LWF and AMP Chain Graphs to Model Interference," Journal of Causal Inference, De Gruyter, vol. 8(1), pages 1-21, January.
    2. Søren Højsgaard & Steffen L. Lauritzen, 2008. "Graphical Gaussian models with edge and vertex symmetries," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 1005-1027, November.
    3. Fitch, A. Marie & Jones, Beatrix, 2012. "The cost of using decomposable Gaussian graphical models for computational convenience," Computational Statistics & Data Analysis, Elsevier, vol. 56(8), pages 2430-2441.
    4. Peña Jose M., 2019. "Unifying Gaussian LWF and AMP Chain Graphs to Model Interference," Journal of Causal Inference, De Gruyter, vol. 8(1), pages 1-21, January.

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