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Comparison of Linear Shrinkage Estimators of a Large Covariance Matrix in Normal and Non-normal Distributions

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  • Yuki Ikeda

    (Graduate School of Economics, The University of Tokyo)

  • Tatsuya Kubokawa

    (Faculty of Economics, The University of Tokyo)

  • Muni S. Srivastava

    (Department of Statistics, University of Toronto)

Abstract

The problem of estimating the large covariance matrix of both normal and non-normal distributions is addressed. In convex combinations of the sample covariance　matrix and the identity matrix multiplied by a scalor statistic, we suggest a new　estimator of the optimal weight based on exact or approximately unbiased estimators of the numerator and denominator of the optimal weight in non-normal cases.　　It is also demonstrated that the estimators given in the literature have second-order biases. It is numerically shown that the proposed estimator has a good risk　performance. --

Suggested Citation

  • Yuki Ikeda & Tatsuya Kubokawa & Muni S. Srivastava, 2015. "Comparison of Linear Shrinkage Estimators of a Large Covariance Matrix in Normal and Non-normal Distributions," CIRJE F-Series CIRJE-F-970, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2015cf970
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    References listed on IDEAS

    as
    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.
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    3. Srivastava, Muni S. & Kollo, Tõnu & von Rosen, Dietrich, 2011. "Some tests for the covariance matrix with fewer observations than the dimension under non-normality," Journal of Multivariate Analysis, Elsevier, vol. 102(6), pages 1090-1103, July.
    4. Jushan Bai & Shuzhong Shi, 2011. "Estimating High Dimensional Covariance Matrices and its Applications," Annals of Economics and Finance, Society for AEF, vol. 12(2), pages 199-215, November.
    5. Ledoit, Olivier & Wolf, Michael, 2003. "Improved estimation of the covariance matrix of stock returns with an application to portfolio selection," Journal of Empirical Finance, Elsevier, vol. 10(5), pages 603-621, December.
    6. Muni S. Srivastava & Hirokazu Yanagihara & Tatsuya Kubokawa, 2014. "Tests for Covariance Matrices in High Dimension with Less Sample Size," CIRJE F-Series CIRJE-F-933, CIRJE, Faculty of Economics, University of Tokyo.
    7. Michael J. Daniels & Robert E. Kass, 2001. "Shrinkage Estimators for Covariance Matrices," Biometrics, The International Biometric Society, vol. 57(4), pages 1173-1184, December.
    8. 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.
    9. 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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