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Error covariance matrix estimation using ridge estimator

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  • Luo, June
  • Kulasekera, K.B.
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    Abstract

    This article considers sparse covariance matrix estimation of high dimension. In contrast to the existing methods which are based on the residual estimation from least squares estimator, we utilize residuals from ridge estimator with the adaptive thresholding technique to estimate the error covariance matrix in high dimensional factor model. By obtaining the explicit convergence rates of the ridge estimator under regularity conditions, we formulated our thresholding estimator of the true covariance matrix. Our thresholding estimator can be applied to more scenarios and is shown to have comparable rate of convergence to Fan et al. (2011).

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    File URL: http://www.sciencedirect.com/science/article/pii/S0167715212003483
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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 83 (2013)
    Issue (Month): 1 ()
    Pages: 257-264

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    Handle: RePEc:eee:stapro:v:83:y:2013:i:1:p:257-264

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    Related research

    Keywords: High dimension; Error covariance matrix; Ridge estimation; Asymptotic property;

    References

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    1. Cai, Tony & Liu, Weidong, 2011. "Adaptive Thresholding for Sparse Covariance Matrix Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 672-684.
    2. Luo, June, 2012. "Asymptotic efficiency of ridge estimator in linear and semiparametric linear models," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 58-62.
    3. Luo, June, 2010. "The discovery of mean square error consistency of a ridge estimator," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 343-347, March.
    4. Fan, Jianqing & Fan, Yingying & Lv, Jinchi, 2008. "High dimensional covariance matrix estimation using a factor model," Journal of Econometrics, Elsevier, vol. 147(1), pages 186-197, November.
    5. Rothman, Adam J. & Levina, Elizaveta & Zhu, Ji, 2009. "Generalized Thresholding of Large Covariance Matrices," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 177-186.
    6. Shao, Jun & Chow, Shein-Chung, 2007. "Variable screening in predicting clinical outcome with high-dimensional microarrays," Journal of Multivariate Analysis, Elsevier, vol. 98(8), pages 1529-1538, September.
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