A new scale-invariant test for two-sample problems for high-dimensional data is proposed
and studied. Under some regularity conditions and the null hypothesis, the proposed test
statistic and a chi-square-type mixture are shown to have the same limiting distribution after
they are normalized. The limiting distribution can be normal or non-normal, depending on
the underlying covariance structure of the high-dimensional data. To approximate the null
distribution of the proposed test, the well-known Welch-Satterthwaite chi-square …