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Asymptotically Normal and Efficient Estimation of Covariate-Adjusted Gaussian Graphical Model

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  • Mengjie Chen
  • Zhao Ren
  • Hongyu Zhao
  • Harrison Zhou

Abstract

We propose an asymptotically normal and efficient procedure to estimate every finite subgraph for covariate-adjusted Gaussian graphical model. As a consequence, a confidence interval as well as p -value can be obtained for each edge. The procedure is tuning-free and enjoys easy implementation and efficient computation through parallel estimation on subgraphs or edges. We apply the asymptotic normality result to perform support recovery through edge-wise adaptive thresholding. This support recovery procedure is called ANTAC, standing for asymptotically normal estimation with thresholding after adjusting covariates. ANTAC outperforms other methodologies in the literature in a range of simulation studies. We apply ANTAC to identify gene--gene interactions using an eQTL dataset. Our result achieves better interpretability and accuracy in comparison with a state-of-the-art method. Supplementary materials for the article are available online.

Suggested Citation

  • Mengjie Chen & Zhao Ren & Hongyu Zhao & Harrison Zhou, 2016. "Asymptotically Normal and Efficient Estimation of Covariate-Adjusted Gaussian Graphical Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(513), pages 394-406, March.
    • Handle: RePEc:taf:jnlasa:v:111:y:2016:i:513:p:394-406
    DOI: 10.1080/01621459.2015.1010039
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    Cited by:

    1. Xiao Guo & Hai Zhang, 2020. "Sparse directed acyclic graphs incorporating the covariates," Statistical Papers, Springer, vol. 61(5), pages 2119-2148, October.
    2. 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.
    3. Guido Consonni & Luca La Rocca & Stefano Peluso, 2017. "Objective Bayes Covariate-Adjusted Sparse Graphical Model Selection," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(3), pages 741-764, September.
    4. Zemin Zheng & Jinchi Lv & Wei Lin, 2021. "Nonsparse Learning with Latent Variables," Operations Research, INFORMS, vol. 69(1), pages 346-359, January.
    5. Shanghong Xie & Xiang Li & Peter McColgan & Rachael I. Scahill & Donglin Zeng & Yuanjia Wang, 2020. "Identifying disease‐associated biomarker network features through conditional graphical model," Biometrics, The International Biometric Society, vol. 76(3), pages 995-1006, September.
    6. Adel Javanmard & Jason D. Lee, 2020. "A flexible framework for hypothesis testing in high dimensions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(3), pages 685-718, July.
    7. Zemin Zheng & Jie Zhang & Yang Li, 2022. "L 0 -Regularized Learning for High-Dimensional Additive Hazards Regression," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2762-2775, September.

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