The Annals of Statistics· 2013Q1
Maximum lilkelihood estimation in the $\beta$-model
- 93citations
- Q1SCImago
- 2013year
Short summary
New conditions are derived for the existence of maximum likelihood estimators (MLEs) in the $\beta$-model for random graphs, based on the polytope of degree sequences.
AI-generated from the title and abstract; the full text is not read.
Key points
- Derives necessary and sufficient conditions for MLE existence in the $\beta$-model using degree sequence polytopes.
- Characterizes sample points leading to non-existent MLEs.
- Formulates conditions guaranteeing MLE existence with probability tending to one as the number of nodes increases.
AI-generated from the title and abstract; the full text is not read.
Abstract
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.
The authors' abstract, as published at the source. The Annals of Statistics, 2013 · DOI ↗
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Field: Discrete Mathematics and Combinatorics
Discrete Mathematics and CombinatoricsMathematics