A Stein Goodness of fit Test for Exponential Random Graph Models

• URL: http://arxiv.org/abs/2103.00580v1
• Date: Sun, 28 Feb 2021 18:16:41 GMT
• Title: A Stein Goodness of fit Test for Exponential Random Graph Models
• Authors: Wenkai Xu and Gesine Reinert
• Abstract summary: We propose and analyse a novel nonparametric goodness of fit testing procedure for exchangeable exponential random graph models. The test determines how likely it is that the observation is generated from a target unnormalised ERGM density.
• Score: 5.885020100736158
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose and analyse a novel nonparametric goodness of fit testing procedure for exchangeable exponential random graph models (ERGMs) when a single network realisation is observed. The test determines how likely it is that the observation is generated from a target unnormalised ERGM density. Our test statistics are derived from a kernel Stein discrepancy, a divergence constructed via Steins method using functions in a reproducing kernel Hilbert space, combined with a discrete Stein operator for ERGMs. The test is a Monte Carlo test based on simulated networks from the target ERGM. We show theoretical properties for the testing procedure for a class of ERGMs. Simulation studies and real network applications are presented.

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