On a complete and sufficient statistic for the correlated Bernoulli random graph model

Inference on vertex-aligned graphs is of wide theoretical and practical importance. There are, however, few flexible tractable statistical models for correlated graphs, even fewer comprehensive approaches to parametric inference data arising from such graphs. In this paper, we consider the Bernoulli random graph model (allowing different coefficients edge correlations pairs vertices), introduce a new variance-reducing technique—called balancing—that can refine estimators parameters. Specifically, construct disagreement statistic show that it complete sufficient; balancing be interpreted as Rao-Blackwellization with statistic. We unbiased functions parameters, generates uniformly minimum variance (UMVUEs). However, when parameters do not exist—which, prove, case both heterogeneity correlation total parameters—balancing still useful, lowers mean squared error. particular, demonstrate how improve efficiency alignment strength estimator correlation, parameter plays critical role in matchability matching runtime complexity.