Binary and Re-search Signal Region Detection in High Dimensions

Signal region detection is one of the challenging problems in modern statistics and has broad applications especially in genetic studies. We propose a novel approach effectively coupling with high-dimensional test, which is distinct from existing methods based on scan or knockoff statistics. The idea is to conduct binary segmentation with re-search and arrangement based on a sequence of dynamic tests to increase detection accuracy and reduce computation. Theoretical and empirical studies demonstrate that our approach enjoys favorable theoretical guarantees with fewer restrictions and exhibits superior numerical performance with faster computation. Compared to scan-based methods, our procedure is capable of detecting shorter or longer regions with unbalanced signal strengths while allowing for more dependence structures. Relative to the knockoff framework that only controls false discovery rate, our approach attains higher detection accuracy while controlling the family-wise error rate. Utilizing the UK Biobank data to identify the genetic regions related to breast cancer, we confirm previous findings and meanwhile, identify a number of new regions which suggest strong association with risk of breast cancer and deserve further investigation.