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Inference for nonparanormal partial correlation via regularized rank‐based nodewise regression

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  • Haoyan Hu
  • Yumou Qiu

Abstract

Partial correlation is a common tool in studying conditional dependence for Gaussian distributed data. However, partial correlation being zero may not be equivalent to conditional independence under non‐Gaussian distributions. In this paper, we propose a statistical inference procedure for partial correlations under the high‐dimensional nonparanormal (NPN) model where the observed data are normally distributed after certain monotone transformations. The NPN partial correlation is the partial correlation of the normal transformed data under the NPN model, which is a more general measure of conditional dependence. We estimate the NPN partial correlations by regularized nodewise regression based on the empirical ranks of the original data. A multiple testing procedure is proposed to identify the nonzero NPN partial correlations. The proposed method can be carried out by a simple coordinate descent algorithm for lasso optimization. It is easy‐to‐implement and computationally more efficient compared to the existing methods for estimating NPN graphical models. Theoretical results are developed to show the asymptotic normality of the proposed estimator and to justify the proposed multiple testing procedure. Numerical simulations and a case study on brain imaging data demonstrate the utility of the proposed procedure and evaluate its performance compared to the existing methods. Data used in preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database.

Suggested Citation

  • 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.
  • Handle: RePEc:bla:biomet:v:79:y:2023:i:2:p:1173-1186
    DOI: 10.1111/biom.13624
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    1. Mai, Qing & Zou, Hui, 2015. "Sparse semiparametric discriminant analysis," Journal of Multivariate Analysis, Elsevier, vol. 135(C), pages 175-188.
    2. 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.
    3. Peng, Jie & Wang, Pei & Zhou, Nengfeng & Zhu, Ji, 2009. "Partial Correlation Estimation by Joint Sparse Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 735-746.
    4. Chang, Jinyuan & Qiu, Yumou & Yao, Qiwei & Zou, Tao, 2018. "Confidence regions for entries of a large precision matrix," Journal of Econometrics, Elsevier, vol. 206(1), pages 57-82.
    5. Chang, Jinyuan & Qiu, Yumou & Yao, Qiwei & Zou, Tao, 2018. "Confidence regions for entries of a large precision matrix," LSE Research Online Documents on Economics 87513, London School of Economics and Political Science, LSE Library.
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