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Title: Concentration and Consistency Results for Canonical and Curved Exponential-Family Models of Random Graphs
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 exponentialfamily 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.  more » « less
Award ID(s):
1812119 1513644
PAR ID:
10094996
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Annals of statistics
ISSN:
0090-5364
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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