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

Weinan Wang, T. Tony Cai, Wenguang Sun

Abstract:

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 infer-
ence 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 in-
formation 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.