High-dimensional factor analysis for network-linked data
针对网络关联观测数据，提出一种广义因子模型，同时刻画网络结构与高维变量间的依赖关系，并开发高效估计与假设检验方法，适用于经济学、社会学等领域的网络数据分析。
Summary Factor analysis is a statistical tool widely used in many disciplines, such as psychology, economics and sociology. As observations linked by networks become increasingly common, incorporating network structures into factor analysis is an important problem that remains open. This article focuses on high-dimensional factor analysis involving network-connected observations, and we propose a generalized factor model with latent factors that account for both the network structure and the dependence structure among high-dimensional variables. These latent factors can be shared by the high-dimensional variables and the network, or exclusively applied to either of them. We develop a computationally efficient estimation procedure and establish asymptotic inferential theories. Notably, we show that by borrowing information from the network, the proposed estimator of the factor loading matrix achieves optimal asymptotic variance under much milder identifiability constraints than in existing literature. Furthermore, we develop a hypothesis testing procedure to tackle the challenge of discerning the structures of the shared and individual latent factors. The finite-sample performance of the proposed method is demonstrated through simulation studies and a real-world dataset involving a statistician coauthorship network.