Adaptive Group-combined P-values Test for Two-sample Location Problem with Applications to Microarray Data

The purpose of this article is to propose a test for two-sample location problem in high-dimensional data. In general highdimensional case, the data dimension can be much larger than the sample size and the underlying distribution may be far from normal. Existing tests requiring explicit relationship between the data dimension and sample size or designed for multivariate normal distributions may lose power significantly and even yield type I error rates strayed from nominal levels. To overcome this issue, we propose an adaptive group p-values combination test which is robust against both high dimensionality and normality. Simulation studies show that the proposed test controls type I error rates correctly and outperforms some existing tests in most situations. An Ageing Human Brain Microarray data are used to further exemplify the method.