Covariate‐assisted ranking and screening for large‐scale two‐sample inference

Two‐sample multiple testing has a wide range of applications. The conventional practice first reduces the original observations to a vector of p‐values and then chooses a cut‐off to adjust for multiplicity. However, this data reduction step could cause significant loss of information and thus lead to suboptimal testing procedures. We introduce a new framework for two‐sample multiple testing by incorporating a carefully constructed auxiliary variable in inference to improve the power. A data‐driven multiple‐testing procedure is developed by employing a covariate‐assisted ranking and screening (CARS) approach that optimally combines the information from both the primary and the auxiliary variables. The proposed CARS procedure is shown to be asymptotically valid and optimal for false discovery rate control. The procedure is implemented in the R package CARS. Numerical results confirm the effectiveness of CARS in false discovery rate control and show that it achieves substantial power gain over existing methods. CARS is also illustrated through an application to the analysis of a satellite imaging data set for supernova detection.