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February 2020 Concentration and consistency results for canonical and curved exponential-family models of random graphs
Michael Schweinberger, Jonathan Stewart
Ann. Statist. 48(1): 374-396 (February 2020). DOI: 10.1214/19-AOS1810

Abstract

Statistical inference for exponential-family models of random graphs with dependent edges is challenging. We stress the importance of additional structure and show that additional structure facilitates statistical inference. A simple example of a random graph with additional structure is a random graph with neighborhoods and local dependence within neighborhoods. We develop the first concentration and consistency results for maximum likelihood and $M$-estimators of a wide range of canonical and curved exponential-family models of random graphs with local dependence. All results are nonasymptotic and applicable to random graphs with finite populations of nodes, although asymptotic consistency results can be obtained as well. In addition, we show that additional structure can facilitate subgraph-to-graph estimation, and present concentration results for subgraph-to-graph estimators. As an application, we consider popular curved exponential-family models of random graphs, with local dependence induced by transitivity and parameter vectors whose dimensions depend on the number of nodes.

Citation

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Michael Schweinberger. Jonathan Stewart. "Concentration and consistency results for canonical and curved exponential-family models of random graphs." Ann. Statist. 48 (1) 374 - 396, February 2020. https://doi.org/10.1214/19-AOS1810

Information

Received: 1 January 2018; Revised: 1 December 2018; Published: February 2020
First available in Project Euclid: 17 February 2020

zbMATH: 07196543
MathSciNet: MR4065166
Digital Object Identifier: 10.1214/19-AOS1810

Subjects:
Primary: 05C80
Secondary: 62B05, 62F10, 91D30

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.48 • No. 1 • February 2020
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