Analysis of Heterogeneous Networks with Unknown Dependence Structure

In multiple heterogeneous networks, developing a model that considers both individual and shared structures is crucial for improving estimation efficiency and interpretability. In this paper, we introduce a semi-parametric individual network autoregressive model. We allow autoregression and regression coefficients to vary across networks with subgroup structure, and integrate both covariates and node relationships into network dependence using a single-index structure with unknown links. To estimate all individual and commonly shared parameters and functions, we introduce a novel penalized semiparametric approach based on the generalized method of moments. Theoretically, our proposed semiparametric estimator for heterogeneous networks exhibits estimation and selection consistency under regular conditions. Numerical experiments are conducted to illustrate the effectiveness of the proposed estimator. The proposed method is applied to analyze patient distribution in hospitals to further demonstrate its utility.