Abstract: Network analyses are becoming increasingly popular in a wide range disciplines, including social science, finance, and genetics. In practice, it is common to collect numerous covariates along with the response variable. Because the network structure means the responses at different nodes are no longer independent, existing screening methods may not perform well for network data. Therefore, we propose a network-based sure independence screening (NW-SIS) method that explicitly considers the network structure. The strong screening consistency property of the NW-SIS method is rigorously established. Furthermore, we estimate the network effect and establish the -consistency of the estimator. The finite-sample performance of the proposed method is assessed using a simulation study and an empirical analysis of a data set from the Chinese stock market.

Key words and phrases: Feature screening, network autoregression, network structure, strong screening consistency.