Adaptive Selection for False Discovery Rate Control Leveraging Symmetry

Controlling the false discovery rate (FDR) in high-dimensional multiple testing has recently been advanced through mirror statistics via knockoff and data splitting. However, these approaches primarily emphasize the symmetry structure of the one-dimensional mirror statistics while inadvertently overlooking the distribution information from non-null features when determining the rejection region, potentially causing a power loss. To tackle this challenge, we present a novel framework termed <i>symmetry-based adaptive selection</i> (SAS), which leverages the symmetry property of the two-dimensional statistics associated with the null features to estimate the local FDR and thereby determine the rejection region. We provide theoretical evidence for the asymptotic validity of FDR control and emphasize the superior power performance of our proposed SAS. Extensive numerical results from both synthetic experiments and two real-world datasets demonstrate that the proposed SAS achieves satisfactory FDR control and significant power improvements over existing methods.