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A Stein Goodness-of-test for Exponential Random Graph Models

Wenkai Xu · Gesine Reinert

Keywords: [ Learning Theory and Statistics ] [ Frequentist Methods ]


We propose and analyse a novel nonparametric goodness-of-fit testing procedure for ex-changeable exponential random graph model (ERGM) 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 of kernel Stein discrepancy, a divergence constructed via Stein’s method using functions from a reproducing kernel Hilbert space (RKHS), combined with a discrete Stein operator for ERGMs. The test is a Monte Carlo test using simulated networks from the target ERGM. We show theoretical properties for the testing procedure w.r.t a class of ERGMs. Simulation studies and real network applications are presented.

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