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Linear shrinkage estimation of large covariance matrices using factor models

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  • Ikeda, Yuki
  • Kubokawa, Tatsuya

Abstract

The problem of estimating a large covariance matrix using a factor model is addressed when both the sample size and the dimension of the covariance matrix tend to infinity. We consider a general class of weighted estimators which includes (i) linear combinations of the sample covariance matrix and the model-based estimator under the factor model, and (ii) linear shrinkage estimators without factors as special cases. The optimal weights in the class are derived, and plug-in weighted estimators are proposed, given that the optimal weights depend on unknown parameters. Numerical results show that our method performs well. Finally, we provide an application to portfolio management.

Suggested Citation

  • Ikeda, Yuki & Kubokawa, Tatsuya, 2016. "Linear shrinkage estimation of large covariance matrices using factor models," Journal of Multivariate Analysis, Elsevier, vol. 152(C), pages 61-81.
    • Handle: RePEc:eee:jmvana:v:152:y:2016:i:c:p:61-81
    DOI: 10.1016/j.jmva.2016.08.001
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    Cited by:

    1. Ruili Sun & Tiefeng Ma & Shuangzhe Liu & Milind Sathye, 2019. "Improved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review," JRFM, MDPI, vol. 12(1), pages 1-34, March.
    2. Nhat Minh Nguyen & Trung Duc Nguyen & Eleftherios I. Thalassinos & Hoang Anh Le, 2022. "The Performance of Shrinkage Estimator for Stock Portfolio Selection in Case of High Dimensionality," JRFM, MDPI, vol. 15(6), pages 1-12, June.
    3. Benoit Oriol & Alexandre Miot, 2023. "Ledoit-Wolf linear shrinkage with unknown mean," Papers 2304.07045, arXiv.org.
    4. Yuasa, Ryota & Kubokawa, Tatsuya, 2020. "Ridge-type linear shrinkage estimation of the mean matrix of a high-dimensional normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 178(C).
    5. Ruili Sun & Tiefeng Ma & Shuangzhe Liu, 2018. "A Stein-type shrinkage estimator of the covariance matrix for portfolio selections," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(8), pages 931-952, November.
    6. Ruili Sun & Tiefeng Ma & Shuangzhe Liu, 2020. "Portfolio selection: shrinking the time-varying inverse conditional covariance matrix," Statistical Papers, Springer, vol. 61(6), pages 2583-2604, December.

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