Abstract:

Recently, several non-scale and scale-invariant tests have been proposed for two-sample problems for high-dimensional data. Most of them impose strong assumptions on the underlying covariance matrix so that their test statistics are asymptotically normally distributed. However, in practice, these assumptions may not be satisfied or hardly be checked so that these tests may not be able to maintain the nominal  size well. In this paper, we propose a simple scale-invariant two-sample test which has  good size control and power without imposing strong assumptions on the underlying covariance or correlation matrix.  A simulation study and a real data example  demonstrate the good performance of the proposed test, via comparing it  against several well-known non-scale  and scale-invariant tests.