Directional false discovery rate control via debiased and distributed procedures in Gaussian graphical models

In this paper, a multiple testing procedure is established for the conditional dependence in Gaussian graphical models. In practice, it is important to determine whether the conditional dependence between variables is positive or negative. However, there are several challenges to building statistics for testing using sample data. For instance, due to privacy concerns, one is not able to aggregate different datasets from several locations in one single location. In this study, different test statistics are constructed using debiased and distributed estimators to address this problem in a multiple testing framework. It is shown that, under mild conditions, the proposed procedure can control asymptotically the directional false discovery rate, which focuses on the sign of the estimation, at a prespecified level. An asymptotic power equal to one is also attainable under mild conditions on the non-zero entries of the precision matrix. Different simulation scenarios and real data examples are used to investigate the performance of the proposed procedure and to confirm the theoretical results.