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May 2020 Degeneracy in sparse ERGMs with functions of degrees as sufficient statistics
Sumit Mukherjee
Bernoulli 26(2): 1016-1043 (May 2020). DOI: 10.3150/19-BEJ1135

Abstract

A sufficient criterion for “non-degeneracy” is given for Exponential Random Graph Models on sparse graphs with sufficient statistics which are functions of the degree sequence. This criterion explains why statistics such as alternating $k$-star are non-degenerate, whereas subgraph counts are degenerate. It is further shown that this criterion is “almost” tight. Existence of consistent estimates is then proved for non-degenerate Exponential Random Graph Models.

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Sumit Mukherjee. "Degeneracy in sparse ERGMs with functions of degrees as sufficient statistics." Bernoulli 26 (2) 1016 - 1043, May 2020. https://doi.org/10.3150/19-BEJ1135

Information

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

zbMATH: 07166555
MathSciNet: MR4058359
Digital Object Identifier: 10.3150/19-BEJ1135

Keywords: Degeneracy , ERGM , normalizing constant , sparse graphs

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

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Vol.26 • No. 2 • May 2020
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