  Network structure is growing popular for capturing the intrinsic relationship
between large-scale variables. In the paper we propose to improve the
estimation accuracy for large-dimensional factor model when a network structure
between individuals is observed. To fully excavate the prior network
information, we construct two different penalties to regularize the factor
loadings and shrink the idiosyncratic errors. Closed-form solutions are
provided for the penalized optimization problems. Theoretical results
demonstrate that the modified estimators achieve faster convergence rates and
lower asymptotic mean squared errors when the underlying network structure
among individuals is correct. An interesting finding is that even if the priori
network is totally misleading, the proposed estimators perform no worse than
conventional state-of-art methods. Furthermore, to facilitate the practical
application, we propose a data-driven approach to select the tuning parameters,
which is computationally efficient. We also provide an empirical criterion to
determine the number of common factors. Simulation studies and application to
the S&P100 weekly return dataset convincingly illustrate the superiority and
adaptivity of the new approach.
