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

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.

• eQTL
• Gene regulatory network
• High-dimensional statistics
• Precision matrix estimation
• Sparsity
• Support recovery.