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April 2013 Consistency under sampling of exponential random graph models
Cosma Rohilla Shalizi, Alessandro Rinaldo
Ann. Statist. 41(2): 508-535 (April 2013). DOI: 10.1214/12-AOS1044


The growing availability of network data and of scientific interest in distributed systems has led to the rapid development of statistical models of network structure. Typically, however, these are models for the entire network, while the data consists only of a sampled sub-network. Parameters for the whole network, which is what is of interest, are estimated by applying the model to the sub-network. This assumes that the model is consistent under sampling, or, in terms of the theory of stochastic processes, that it defines a projective family. Focusing on the popular class of exponential random graph models (ERGMs), we show that this apparently trivial condition is in fact violated by many popular and scientifically appealing models, and that satisfying it drastically limits ERGM’s expressive power. These results are actually special cases of more general results about exponential families of dependent random variables, which we also prove. Using such results, we offer easily checked conditions for the consistency of maximum likelihood estimation in ERGMs, and discuss some possible constructive responses.


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Cosma Rohilla Shalizi. Alessandro Rinaldo. "Consistency under sampling of exponential random graph models." Ann. Statist. 41 (2) 508 - 535, April 2013.


Published: April 2013
First available in Project Euclid: 26 April 2013

zbMATH: 1269.91066
MathSciNet: MR3099112
Digital Object Identifier: 10.1214/12-AOS1044

Primary: 62B05 , 91D30
Secondary: 60G51 , 62M09 , 62M99

Keywords: exponential family , exponential random graph model , Independent increments , network models , network sampling , projective family , sufficient statistics

Rights: Copyright © 2013 Institute of Mathematical Statistics


Vol.41 • No. 2 • April 2013
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