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

Mengjie Chen, Zhao Ren, Hongyu Zhao and Harrison Zhou

Journal of the American Statistical Association, 2016, vol. 111, issue 513, 394-406

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.

Date: 2016
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DOI: 10.1080/01621459.2015.1010039

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