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 detection methods with multilayer FDR control generally rely on valid p-values or knockoff statistics, which can be not flexible, powerful and stable 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, leveraging a generalized e-filter, and adopting a stabilization treatment with power enhancement. This method flexibly incorporates diverse base detection procedures at different resolutions to provide consistent, powerful, and stable results, while controlling FDR at multiple resolutions simultaneously. Statistical properties of multilayer filtering procedure encompassing one-bit property, multilayer FDR control, and stability guarantee are established. We also develop several examples for SFEFP such as the eDS-filter. Simulation studies and the analysis of HIV mutation data demonstrate the efficacy of SFEFP.