A p-value based dimensionality reduction test for high dimensional means

With the rapid development of modern computing techniques, high-dimensional data are increasingly encountered in many studies. In this paper, we propose a three-step method to study the mean testing problem. The proposed test is based on the p-values calculated from the univariate tests and the dimension reduction method. Since it does not require explicit conditions of data dimension and sample size, we can use it to solve the mean testing problem of high-dimensional data, especially when the data dimension is much larger than the sample size. The new method can be implemented for the normal and non-normal distribution, which has a wide application. Various simulations are conducted to compare the testing power of the new method and the existing tests. The comparison shows that the new method has higher testing power. We also apply the proposed method to a real example of gene expression data.