An adaptive two-sample test for high-dimensional means

Several two-sample tests for high-dimensional data have been proposed recently, but they are powerful only against certain limited alternative hypotheses. In practice, since the true alternative hypothesis is unknown, it is unclear how to choose a powerful test. We propose an adaptive test that maintains high power across a wide range of situations, and study its asymptotic properties. Its finite sample performance is compared with existing tests. We apply it and other tests to detect possible associations between bipolar disease and a large number of single nucleotide polymorphisms on each chromosome based on a genome-wide association study dataset. Numerical studies demonstrate the superior performance and high power of the proposed test across a wide spectrum of applications.