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

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

2005-08-15

arxiv.org/abs/math/0508266v2

Scandinavian Journal of Statistics 2006, Vol. 33, No. 2, 247-257

Mathematics

Statistics Theory

15 pages, article will appear in Scandinavian Journal of Statistics

Scientific paper

10.1111/j.1467-9469.2006.00482.x

The AMP Markov property is a recently proposed alternative Markov property for chain graphs. In the case of continuous variables with a joint multivariate Gaussian distribution, it is the AMP rather than the earlier introduced LWF 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.

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