Covariate-Assisted Two-Sample Sparse 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 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 talk, we introduce a new framework for two-sample multiple testing by incorporating a carefully constructed auxiliary variable in inference to improve the power. The first part of the talk considers the optimal inference under independence. A data-driven multiple testing procedure is developed by employing a covariate-assisted ranking and screening approach to combine the information from both the primary and auxiliary variables. The second part of the talk discusses a simple framework for incorporating the auxiliary covariates under dependence. We establish general conditions under which the proposed methods are asymptotically valid for false discovery rate control. Numerical results demonstrate that existing methods can be significantly improved by the proposed framework.