Two-sample mean vector projection test in high-dimensional data

Statistical hypothesis testing for high-dimensional data poses challenges in recent inference. The Hotelling test is commonly applied to the comparison of mean vectors with a fixed dimension of mean vectors, but becomes unavailable when the dimension diverges or greater than sample sizes. For the high-dimensional regimes, we propose a two-sample mean vector test statistic by adding a projection term based on the Euclidean norm of the mean vectors. The projection term improves power and ensures the validity for dimensions greater than sample sizes, without relying on any inverse matrices. The proposed projection statistic, suitably standardized, approximates a standard normal distribution under mild conditions. Extensive simulation results, under different scenarios, show that the proposed approach enjoys a comparable Type I error and an improved efficiency power. We further illustrate its application by testing the equality of two acute lymphocytic leukemia genetic data and a significant test of the “Sell in May and Go Away” effect in China A stock market.