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May 2020 Consistent structure estimation of exponential-family random graph models with block structure
Michael Schweinberger
Bernoulli 26(2): 1205-1233 (May 2020). DOI: 10.3150/19-BEJ1153

Abstract

We consider the challenging problem of statistical inference for exponential-family random graph models based on a single observation of a random graph with complex dependence. To facilitate statistical inference, we consider random graphs with additional structure in the form of block structure. We have shown elsewhere that when the block structure is known, it facilitates consistency results for $M$-estimators of canonical and curved exponential-family random graph models with complex dependence, such as transitivity. In practice, the block structure is known in some applications (e.g., multilevel networks), but is unknown in others. When the block structure is unknown, the first and foremost question is whether it can be recovered with high probability based on a single observation of a random graph with complex dependence. The main consistency results of the paper show that it is possible to do so under weak dependence and smoothness conditions. These results confirm that exponential-family random graph models with block structure constitute a promising direction of statistical network analysis.

Citation

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Michael Schweinberger. "Consistent structure estimation of exponential-family random graph models with block structure." Bernoulli 26 (2) 1205 - 1233, May 2020. https://doi.org/10.3150/19-BEJ1153

Information

Received: 1 March 2018; Revised: 1 March 2019; Published: May 2020
First available in Project Euclid: 31 January 2020

zbMATH: 07166561
MathSciNet: MR4058365
Digital Object Identifier: 10.3150/19-BEJ1153

Rights: Copyright © 2020 Bernoulli Society for Mathematical Statistics and Probability

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Vol.26 • No. 2 • May 2020
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