General linear hypothesis testing of high-dimensional mean vectors with unequal covariance matrices based on random integration

This paper is devoted to the study of the general linear hypothesis testing (GLHT) problem of multi-sample high-dimensional mean vectors. For the GLHT problem, we introduce a test statistic based on $L^2$-norm and random integration method, and deduce the asymptotic distribution of the statistic under given conditions. Finally, the potential advantages of our test statistics are verified by numerical simulation studies and examples.