Asymptotic normality in the maximum entropy models on graphs with an increasing number of parameters. (English) Zbl 1304.62038
Summary: Maximum entropy models, motivated by applications in neuron science, are natural generalizations of the \(\beta\)-model to weighted graphs. Similar to the \(\beta\)-model, each vertex in maximum entropy models is assigned a potential parameter, and the degree sequence is the natural sufficient statistic. C. Hillar and A. Wibisono [“Maximum entropy distributions on graphs”, Preprint, arXiv:1301.3321] have proved the consistency of the maximum likelihood estimators. In this paper, we further establish the asymptotic normality for any finite number of the maximum likelihood estimators in the maximum entropy models with three types of edge weights, when the total number of parameters goes to infinity. Simulation studies are provided to illustrate the asymptotic results.
MSC:
| 62E20 | Asymptotic distribution theory in statistics |
| 62F12 | Asymptotic properties of parametric estimators |
Keywords:
maximum entropy models; maximum likelihood estimator; asymptotic normality; increasing number of parametersReferences:
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