Title: Low-rank and sparse network regression Authors:  Weining Wang - University of Bristol (United Kingdom) [presenting]
Abstract: Spillover effects in spatial network models are analyzed under settings where measurement noises might contaminate the neighborhood (i.e., adjacency) matrix. We propose to adopt the low-rank and sparse structure to capture the stylized network pattern in empirical datasets. We develop a robust estimation framework via regularization techniques: the Least Absolute Shrinkage and Selection Operator (LASSO) for the sparse component and a nuclear norm penalty for the low-rank component. We propose two estimators: (1) A two-stage procedure that first de-noises the adjacency matrix via regularization and subsequently integrates the purified network to regression analysis, and (2) A single-step supervised Generalized Method of Moments (GMM) estimator jointly estimates the regression parameters and refines the network structure. Simulation evidence underscores the superiority of our approach. In scenarios with noisy networks, our method reduces the root mean squared error (RMSE) of coefficient estimates by $5070\%$ compared to conventional GMM. This advantage is more significant when network contamination is endogenous, a common challenge in empirical settings where measurement errors correlate with the observed outcomes.