An exact test about the covariance matrix

In the present paper, we propose an exact test on the structure of the covariance matrix. In its development the properties of the Wishart distribution are used. Unlike the classical likelihood-ratio type tests and the tests based on the empirical distance, whose statistics depend on the total variance and the generalized variance only, the proposed approach provides more information about the changes in the covariance matrix. Via an extensive simulation study the new approach is compared with the existent asymptotic tests.