Abstract: We gave  a new method to test the equality of  twosample highdimensional  covariance matrices based on random matrix theory in a highdimensional framework. The results show that using  the central limit theorem for the linear spectral statistics of highdimensional random F-matrices, the limit distribution of the test statistics is given, which is not only suitable for  highdimensional data but also valid for nonnormal cases.

Key words: highdimensional data, twosample covariance test,  , highdimensional F-matrix, central limit theorem