Estimation and variable selection for high-dimensional spatial data models

Spatiotemporal modeling of networks is of great practical importance, with modern applications in epidemiology and social network analysis. Despite rapid methodological advances, how to effectively and efficiently estimate the parameters of spatial dynamic panel models remains a challenging problem. To tackle this problem, we construct consistent complex least-squares estimators by the eigendecomposition of a spatial weight matrix method originally proposed for undirected networks. We no longer require all eigenvalues and eigenvectors to be real, which is a remarkable achievement as it implies that the proposed method is now applicable to spatiotemporal data modeling of directed networks. Under mild, interpretable conditions, we show that the proposed parameter estimators are consistent and asymptotically normally distributed. We also present a complex orthogonal greedy algorithm for variable selection and rigorously investigate its convergence properties. Moreover, we incorporate fixed effects into the spatial dynamic panel models and provide a model transformation so that the proposed method can also be applied to the transformed model. Extensive simulation studies and data examples demonstrate the effectiveness of the proposed method.