Covariate-adjusted Gaussian graphical model estimation with false discovery rate control

Abstract

Recent genetic/genomic studies have shown that genetic markers can have potential effects on the dependence structure of genes. Motivated by such findings, we are interested in the estimation of covariate-adjusted Gaussian graphical model (CGGM). Most existing approaches depend on regularization techniques, which makes the precise relationship between the regularized parameter and the number of false discovered edges in CGGM estimation ambiguous. In this paper, we formulate CGGM estimation as a multiple testing problem. A new test statistic is introduced and shown to be asymptotic normal null distribution. We then propose a multiple testing procedure for CGGM estimation. The procedure is shown to control the false discovery rate (FDR) at any pre-specified significance level asymptotically. Finally, we provide numerical results to show the performance of our method in both simulation studies and real data analysis.