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High dimensional Gaussian copula graphical model with FDR control

Author

Listed:
  • He, Yong
  • Zhang, Xinsheng
  • Wang, Pingping
  • Zhang, Liwen

Abstract

A multiple testing procedure is proposed to estimate the high dimensional Gaussian copula graphical model and nonparametric rank-based correlation coefficient estimators are exploited to construct the test statistics, which achieve modeling flexibility and estimation robustness. Compared to the existing methods depending on regularization technique, the proposed method avoids the ambiguous relationship between the regularized parameter and the number of false edges in graph estimation. It is proved that the proposed procedure can control the false discovery rate (FDR) asymptotically. Besides theoretical analysis, thorough numerical simulations are conducted to compare the graph estimation performance of the proposed method with some other state-of-the-art methods. The result shows that the proposed method works quite well under both non-Gaussian and Gaussian settings. The proposed method is then applied on a stock market data set to illustrate its empirical usefulness.

Suggested Citation

  • He, Yong & Zhang, Xinsheng & Wang, Pingping & Zhang, Liwen, 2017. "High dimensional Gaussian copula graphical model with FDR control," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 457-474.
    • Handle: RePEc:eee:csdana:v:113:y:2017:i:c:p:457-474
    DOI: 10.1016/j.csda.2016.06.012
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    References listed on IDEAS

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    1. Ming Yuan & Yi Lin, 2007. "Model selection and estimation in the Gaussian graphical model," Biometrika, Biometrika Trust, vol. 94(1), pages 19-35.
    2. Mathias Drton, 2004. "Model selection for Gaussian concentration graphs," Biometrika, Biometrika Trust, vol. 91(3), pages 591-602, September.
    3. Cai, Tony & Liu, Weidong & Luo, Xi, 2011. "A Constrained â„“1 Minimization Approach to Sparse Precision Matrix Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 594-607.
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    Cited by:

    1. Haoyan Hu & Yumou Qiu, 2023. "Inference for nonparanormal partial correlation via regularized rank‐based nodewise regression," Biometrics, The International Biometric Society, vol. 79(2), pages 1173-1186, June.
    2. He, Yong & Zhang, Xinsheng & Zhang, Liwen, 2018. "Variable selection for high dimensional Gaussian copula regression model: An adaptive hypothesis testing procedure," Computational Statistics & Data Analysis, Elsevier, vol. 124(C), pages 132-150.
    3. Yu, Long & He, Yong & Zhang, Xinsheng, 2019. "Robust factor number specification for large-dimensional elliptical factor model," Journal of Multivariate Analysis, Elsevier, vol. 174(C).

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