Homogeneity pursuit in nonparametric heterogeneity model based on network data. (Chinese. English summary) Zbl 07802097

Tang, Yiming; Hu, Shengchang; Long, Yuhang; Huang, Tao

Acta Math. Appl. Sin. 46, No. 6, 963-997 (2023).

Summary: The fixed effects model for network data is built based on the heterogeneity of network nodes, disregarding the homogeneity among nodes. Existing models that consider the homogeneity of network nodes often apply only to specific network data that meets certain conditions. At the same time, current models often overlook the impact of node features on edges or only consider the linear effect of features on edges. In this paper, we propose a nonparametric heterogeneity model and a data driven homogeneity pursuit approach to explore the homogeneity structure of the network data. We theoretically demonstrate the consistency and asymptotic normality of the parametric part and the consistency of the nonparametric part. The proposed model and method are validated by simulations and two real data analyses.

MSC:

62G05	Nonparametric estimation
62G20	Asymptotic properties of nonparametric inference

Keywords:

network data; homogeneity pursuit; nonparametric model; spline