huge (e.g., Facebook, Twitter, Weibo, WeChat, etc). In that case, one has to rely on sampled network data to infer about social intercorrelation. By doing so, network relationships (i.e., edges) involving unsampled nodes are overlooked. This leads to distorted network structure and underestimated social intercorrelation. To solve the problem, we propose here a novel solution. It makes use of the fact that social intercorrelation is typically small. This enables us to approximate the targeting likelihood by its first order Taylor's expansion. Depending on the choice of the likelihood, we obtain respectively an approximate maximum likelihood estimator (AMLE) and paired maximum likelihood estimator (PMLE). We show theoretically that both methods are consistent and asymptotically normal with identical asymptotic efficiency. However, the difference is that PMLE is omputationally superior. Numerical studies based on both simulated and real datasets are presented for illustration purpose.
