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Robust Covariance Estimation for Approximate Factor Models.

Jianqing Fan1,2, Weichen Wang1, Yiqiao Zhong1

  • 1Department of Operations Research and Financial Engineering, Sherrerd Hall, Princeton University, Princeton, NJ 08544, USA.

Journal of Econometrics
|December 15, 2018
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Summary
This summary is machine-generated.

This study introduces a robust covariance estimation method for approximate factor models. The novel framework improves accuracy for observed data, even with non-standard distributions.

Keywords:
Approximate factor modelM-estimatorRobust covariance matrix

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Area of Science:

  • Statistics
  • Econometrics
  • Machine Learning

Background:

  • Covariance estimation is crucial in statistical analysis.
  • Approximate factor models are widely used in econometrics and finance.
  • Robustness is essential for reliable estimation with complex data.

Purpose of the Study:

  • To develop a robust covariance estimation method for approximate factor models with observed factors.
  • To ensure accurate recovery of the observed data's covariance matrix.
  • To extend applicability beyond traditional distributional assumptions.

Main Methods:

  • A novel two-step framework for covariance estimation.
  • Initial estimation of the joint covariance matrix of data and factors.
  • Adaptive Huber loss minimization for initial estimation with bounded fourth moments.

Main Results:

  • The proposed method achieves desired properties for the estimated covariance matrix.
  • The framework is effective for data beyond sub-Gaussian and elliptical distributions.
  • Asymptotic results for adaptive Huber's M-estimator are provided.

Conclusions:

  • The novel framework offers robust covariance estimation under approximate factor models.
  • Adaptive Huber loss minimization enhances applicability to a wider range of data distributions.
  • The method's efficacy is validated through simulations and real-world data analysis.