CARS: Covariate Assisted Ranking and Screening for Large-Scale Two-Sample Inference
T. Tony Cai, Wenguang Sun, and Weinan Wang
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Abstract:
Two-sample multiple testing has a wide range of applications. The conventional practice is to first reduce the original observations to a vector of p-values and then choose a cutoff to adjust for multiplicity. However, this data reduction step could cause significant loss of information and thus lead to suboptimal testing procedures. In this paper, 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 auxiliary variables.
The proposed CARS procedure is shown to be asymptotic valid and optimal for false discovery rate (FDR) control. The procedure is implemented in the R-package CARS. Numerical results confirm the effectiveness of CARS in FDR control and show that it achieves substantial power gain over existing methods. CARS is also illustrated through an application to the analysis of satellite imaging data set for supernova detection.
- Paper: pdf file.