A high-dimensional test for the k-sample Behrens-Fisher problem

In this paper, the problem of testing the equality of the mean vectors of k populations with possibly unknown and unequal covariance matrices is investigated in high-dimensional settings. The null distributions of most existing tests are asymptotically normal which inevitably imposes strong conditions on covariance matrices. However, we assume here only mild additional conditions on the proposed test, which offers much flexibility in practical applications. Additionally, the Welch-Satterthwaite chi 2-approximation we adopted can automatically mimic the shape of the null distribution of the proposed test statistic, while the normal approximation cannot achieve the adaptivity. Finally, an extensive simulation study shows that the proposed test has better performance on both size and power compared with existing methods.