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MAXIMUM LILKELIHOOD ESTIMATION IN THE β-MODEL
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DOI：10.1214/12-AOS1078.png)
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摘要
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We study maximum likelihood estimation for the statistical model for undirected random graphs, known as the beta-model, in which the degree sequences are minimal sufficient statistics. We derive necessary and sufficient conditions, based on the polytope of degree sequences, for the existence of the maximum likelihood estimator (MLE) of the model parameters. We characterize in a combinatorial fashion sample points leading to a nonexistent MLE, and nonestimability of the probability parameters under a nonexistent MLE. We formulate conditions that guarantee that the MLE exists with probability tending to one as the number of nodes increases.
Keyword:
beta-model
polytope of degree sequences
random graphs
maximum likelihood estimator
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