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Target selection in shrinkage estimation of covariance matrix: A structural similarity approach

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  • Wang, Xuanci
  • Zhang, Bin

Abstract

The shrinkage estimator of a high-dimensional covariance matrix relies on a preassigned target matrix during data processing. This paper provides an adaptive approach for selecting the optimal Toeplitz target matrix. We discover a sufficient and necessary condition for characterizing the two kinds of target matrices with the Toeplitz structure, and we propose an adaptive selection algorithm by measuring the similarity between the data and the Toeplitz structure. Numerical simulations and an empirical study on monetary funds verify the effectiveness of the selection approach.

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  • Wang, Xuanci & Zhang, Bin, 2024. "Target selection in shrinkage estimation of covariance matrix: A structural similarity approach," Statistics & Probability Letters, Elsevier, vol. 208(C).
    • Handle: RePEc:eee:stapro:v:208:y:2024:i:c:s0167715224000178
    DOI: 10.1016/j.spl.2024.110048
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    References listed on IDEAS

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    1. Ledoit, Olivier & Wolf, Michael, 2004. "A well-conditioned estimator for large-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 365-411, February.
    2. Joo, Young C. & Park, Sung Y., 2021. "Optimal portfolio selection using a simple double-shrinkage selection rule," Finance Research Letters, Elsevier, vol. 43(C).
    3. Lin, Lijing & Higham, Nicholas J. & Pan, Jianxin, 2014. "Covariance structure regularization via entropy loss function," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 315-327.
    4. Srivastava, Muni S. & Yanagihara, Hirokazu, 2010. "Testing the equality of several covariance matrices with fewer observations than the dimension," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1319-1329, July.
    5. Huang, Chao & Farewell, Daniel & Pan, Jianxin, 2017. "A calibration method for non-positive definite covariance matrix in multivariate data analysis," Journal of Multivariate Analysis, Elsevier, vol. 157(C), pages 45-52.
    6. Chen, Song Xi & Zhang, Li-Xin & Zhong, Ping-Shou, 2010. "Tests for High-Dimensional Covariance Matrices," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 810-819.
    7. Ledoit, Olivier & Wolf, Michael, 2021. "Shrinkage estimation of large covariance matrices: Keep it simple, statistician?," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    8. Ding, Yi & Li, Yingying & Zheng, Xinghua, 2021. "High dimensional minimum variance portfolio estimation under statistical factor models," Journal of Econometrics, Elsevier, vol. 222(1), pages 502-515.
    9. Fisher, Thomas J. & Sun, Xiaoqian & Gallagher, Colin M., 2010. "A new test for sphericity of the covariance matrix for high dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2554-2570, November.
    10. Yang, Yihe & Zhou, Jie & Pan, Jianxin, 2021. "Estimation and optimal structure selection of high-dimensional Toeplitz covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    11. Wei Biao Wu, 2003. "Nonparametric estimation of large covariance matrices of longitudinal data," Biometrika, Biometrika Trust, vol. 90(4), pages 831-844, December.
    12. Furrer, Reinhard & Bengtsson, Thomas, 2007. "Estimation of high-dimensional prior and posterior covariance matrices in Kalman filter variants," Journal of Multivariate Analysis, Elsevier, vol. 98(2), pages 227-255, February.
    13. Fisher, Thomas J. & Sun, Xiaoqian, 2011. "Improved Stein-type shrinkage estimators for the high-dimensional multivariate normal covariance matrix," Computational Statistics & Data Analysis, Elsevier, vol. 55(5), pages 1909-1918, May.
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