High-dimensional projection-based ANOVA test

In bioinformation and medicine, an enormous amount of high-dimensional multi-population data is collected. For the inference of several-samples mean problem, traditional tests do not perform well and many new theories mainly focus on normal distribution and low correlation assumptions. Motivated by the weighted sign test, we propose two projection-based tests which are robust against the choice of correlation matrix. One test utilizes Scheffe's transformation to generate a group of new samples and derives the optimal projection direction. The other test is adaptive to projection direction and is generalized to the assumption of the whole elliptical distribution and independent component model. Further the theoretical properties are deduced and numerical experiments are carried out to examine the finite sample performance. They show that our tests outperform others under certain circumstances.