  Selecting relevant features associated with a given response variable is an
important issue in many scientific fields. Quantifying quality and uncertainty
of a selection result via false discovery rate (FDR) control has been of recent
interest. This paper introduces a way of using data-splitting strategies to
asymptotically control the FDR while maintaining a high power. For each
feature, the method constructs a test statistic by estimating two independent
regression coefficients via data splitting. FDR control is achieved by taking
advantage of the statistic's property that, for any null feature, its sampling
distribution is symmetric about zero. Furthermore, we propose Multiple Data
Splitting (MDS) to stabilize the selection result and boost the power.
Interestingly and surprisingly, with the FDR still under control, MDS not only
helps overcome the power loss caused by sample splitting, but also results in a
lower variance of the false discovery proportion (FDP) compared with all other
methods in consideration. We prove that the proposed data-splitting methods can
asymptotically control the FDR at any designated level for linear and Gaussian
graphical models in both low and high dimensions. Through intensive simulation
studies and a real-data application, we show that the proposed methods are
robust to the unknown distribution of features, easy to implement and
computationally efficient, and are often the most powerful ones amongst
competitors especially when the signals are weak and the correlations or
partial correlations are high among features.
