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Network structure is growing popular for capturing the intrinsic relationshipbetween large-scale variables. In the paper we propose to improve theestimation accuracy for large-dimensional factor model when a network structurebetween individuals is observed. To fully excavate the prior networkinformation, we construct two different penalties to regularize the factorloadings and shrink the idiosyncratic errors. Closed-form solutions areprovided for the penalized optimization problems. Theoretical resultsdemonstrate that the modified estimators achieve faster convergence rates andlower asymptotic mean squared errors when the underlying network structureamong individuals is correct. An interesting finding is that even if the priorinetwork is totally misleading, the proposed estimators perform no worse thanconventional state-of-art methods. Furthermore, to facilitate the practicalapplication, we propose a data-driven approach to select the tuning parameters,which is computationally efficient. We also provide an empirical criterion todetermine the number of common factors. Simulation studies and application tothe S&P100 weekly return dataset convincingly illustrate the superiority andadaptivity of the new approach.

Network-Assisted Estimation for Large-dimensional Factor Model with Guaranteed Convergence Rate Improvement