A Generalized E-Value Feature Detection Method with FDR Control at Multiple Resolutions

Multiple resolutions arise across a range of explanatory features due to domain-specific structures, leading to the formation of feature groups. It follows that the simultaneous detection of significant features and groups aimed at a specific response with false discovery rate (FDR) control stands as a crucial issue, such as the spatial genome-wide association studies. Nevertheless, existing methods such as the multilayer knockoff filter (MKF) generally require a uniform detection approach across resolutions to achieve multilayer FDR control, which can be not powerful or even not applicable in several settings. To fix this issue effectively, this article develops a novel method of stabilized flexible e-filter procedure (SFEFP), by constructing unified generalized e-values, developing a generalized e-filter, and adopting a stabilization treatment. This method flexibly incorporates a wide variety of base detection procedures that operate effectively across different resolutions to provide stable and consistent results, while controlling the false discovery rate at multiple resolutions simultaneously. Furthermore, we investigate the statistical theories of the SFEFP, encompassing multilayer FDR control and stability guarantee. We develop several examples for SFEFP such as eDS-filter and eDS+gKF-filter. Simulation studies demonstrate that the eDS-filter effectively controls FDR at multiple resolutions while either maintaining or enhancing power compared to MKF. The superiority of the eDS-filter is also demonstrated through the analysis of HIV mutation data.