IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v113y2017icp457-474.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947316301499
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2016.06.012?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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).
    3. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Alexandre Belloni & Mingli Chen & Victor Chernozhukov, 2016. "Quantile Graphical Models: Prediction and Conditional Independence with Applications to Systemic Risk," Papers 1607.00286, arXiv.org, revised Oct 2019.
    2. Byrd, Michael & Nghiem, Linh H. & McGee, Monnie, 2021. "Bayesian regularization of Gaussian graphical models with measurement error," Computational Statistics & Data Analysis, Elsevier, vol. 156(C).
    3. Dong Liu & Changwei Zhao & Yong He & Lei Liu & Ying Guo & Xinsheng Zhang, 2023. "Simultaneous cluster structure learning and estimation of heterogeneous graphs for matrix‐variate fMRI data," Biometrics, The International Biometric Society, vol. 79(3), pages 2246-2259, September.
    4. Fan, Jianqing & Feng, Yang & Xia, Lucy, 2020. "A projection-based conditional dependence measure with applications to high-dimensional undirected graphical models," Journal of Econometrics, Elsevier, vol. 218(1), pages 119-139.
    5. Liu, Jianyu & Yu, Guan & Liu, Yufeng, 2019. "Graph-based sparse linear discriminant analysis for high-dimensional classification," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 250-269.
    6. Pei Wang & Shunjie Chen & Sijia Yang, 2022. "Recent Advances on Penalized Regression Models for Biological Data," Mathematics, MDPI, vol. 10(19), pages 1-24, October.
    7. Guanghui Cheng & Zhengjun Zhang & Baoxue Zhang, 2017. "Test for bandedness of high-dimensional precision matrices," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(4), pages 884-902, October.
    8. Wang, Luheng & Chen, Zhao & Wang, Christina Dan & Li, Runze, 2020. "Ultrahigh dimensional precision matrix estimation via refitted cross validation," Journal of Econometrics, Elsevier, vol. 215(1), pages 118-130.
    9. Lin Zhang & Andrew DiLernia & Karina Quevedo & Jazmin Camchong & Kelvin Lim & Wei Pan, 2021. "A random covariance model for bi‐level graphical modeling with application to resting‐state fMRI data," Biometrics, The International Biometric Society, vol. 77(4), pages 1385-1396, December.
    10. Huihang Liu & Xinyu Zhang, 2023. "Frequentist model averaging for undirected Gaussian graphical models," Biometrics, The International Biometric Society, vol. 79(3), pages 2050-2062, September.
    11. Nezakati, Ensiyeh & Pircalabelu, Eugen, 2021. "Unbalanced distributed estimation and inference for precision matrices," LIDAM Discussion Papers ISBA 2021031, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    12. Sheng, Tianhong & Li, Bing & Solea, Eftychia, 2023. "On skewed Gaussian graphical models," Journal of Multivariate Analysis, Elsevier, vol. 194(C).
    13. Tan, Kean Ming & Witten, Daniela & Shojaie, Ali, 2015. "The cluster graphical lasso for improved estimation of Gaussian graphical models," Computational Statistics & Data Analysis, Elsevier, vol. 85(C), pages 23-36.
    14. Hirose, Kei & Fujisawa, Hironori & Sese, Jun, 2017. "Robust sparse Gaussian graphical modeling," Journal of Multivariate Analysis, Elsevier, vol. 161(C), pages 172-190.
    15. Pan, Yuqing & Mai, Qing, 2020. "Efficient computation for differential network analysis with applications to quadratic discriminant analysis," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    16. Bailey, Natalia & Pesaran, M. Hashem & Smith, L. Vanessa, 2019. "A multiple testing approach to the regularisation of large sample correlation matrices," Journal of Econometrics, Elsevier, vol. 208(2), pages 507-534.
    17. Ines Wilms & Jacob Bien, 2021. "Tree-based Node Aggregation in Sparse Graphical Models," Papers 2101.12503, arXiv.org.
    18. Avagyan, Vahe & Nogales, Francisco J., 2014. "Improving the graphical lasso estimation for the precision matrix through roots ot the sample convariance matrix," DES - Working Papers. Statistics and Econometrics. WS ws141208, Universidad Carlos III de Madrid. Departamento de Estadística.
    19. Liu, Weidong & Luo, Xi, 2015. "Fast and adaptive sparse precision matrix estimation in high dimensions," Journal of Multivariate Analysis, Elsevier, vol. 135(C), pages 153-162.
    20. Xingqi Du & Subhashis Ghosal, 2018. "Bayesian Discriminant Analysis Using a High Dimensional Predictor," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(1), pages 112-145, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:113:y:2017:i:c:p:457-474. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.