Finite sample t-tests for high-dimensional means

When sample sizes are small, it becomes challenging for an asymptotic test requiring diverging to maintain accurate Type I error rate. In this paper, we consider one-sample, two-sample and ANOVA tests mean vectors when data high-dimensional but very small. We establish t-distributions of the proposed U-statistics, which only require dimensionality diverge be fixed no less than 3. The rates a wide range dimensionality. Moreover, nonparametric can applied normally distributed or heavy-tailed. Simulation studies confirm theoretical results tests. also apply fMRI dataset demonstrate practical implementation methods.