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

TL;DR

This paper introduces a network-assisted estimation method for large-dimensional factor models that leverages observed network structures to improve accuracy, achieve faster convergence, and maintain robustness even with misleading prior information.

Contribution

The paper proposes a novel penalized estimation approach incorporating network information, with closed-form solutions and a data-driven tuning parameter selection method.

Findings

Faster convergence rates for the proposed estimators.

Lower asymptotic mean squared errors with correct network structure.

Robust performance even when the prior network is misleading.

Abstract

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.