Empirical likelihood for network data

This article develops a concept of nonparametric likelihood for network data based on network moments, and proposes general inference methods by adapting the theory of jackknife empirical likelihood. Our methodology can be used not only to conduct inference on population network moments and parameters in network formation models, but also to implement goodness-of-fit testing, such as testing block size for stochastic block models. Theoretically we show that the jackknife empirical likelihood statistic for acyclic or cyclic subgraph moments loses its asymptotic pivotalness in severely or moderately sparse cases, respectively, and develop a modified statistic to recover pivotalness in such cases. The main advantage of our modified jackknife empirical likelihood method is its validity under weaker sparsity conditions than existing methods although it is computationally more demanding than the unmodified version. Supplementary materials for this article are available online.