Network Assisted Approximate Factor Model Estimation

The factor models are powerful tools for uncovering patterns of similarity or co-movement among individuals, and they have been successfully applied in the fields of finance and biology.However, the classical approximate factor model encounters limitations when dealing with small sample sizes.To overcome this challenge, we leverage auxiliary network information and propose a novel joint quasi-maximum likelihood estimation, which can use the network information flexibly and allow network heterogeneity.The theoretical properties of these estimators are rigorously established.We obtain a new convergence rate, which is faster than the rate of classical maximum likelihood estimators when the sample size is small.Numerous numerical studies have been conducted to evaluate the performance of the proposed methods.