Directional false discovery rate control via distributed procedures for Gaussian graphical models

We propose a multiple testing procedure for conditional dependence in Gaussian graphical models based on a distributed estimator constructed using K local samples. In practice, due to privacy concerns, building test statistics using local data is challenging since one is not able to aggregate the K different datasets from several locations at one single location. In this paper, different test statistics are constructed using debiased and distributed estimators to address the problem in a multiple testing framework. It is shown that under conditions, the proposed procedure can control asymptotically at any pre-specified level the directional false discovery rate, a metric which focuses on the sign of the estimation. An asymptotic power equal to one is also attainable under conditions on the non-zero entries of the precision matrix. Different simulation scenarios and a real data example are used to investigate the performance of the proposed procedure in practice and to verify the theoretical results.