A power function of statistical tests dependent on elementary symmetric polynomials

Statistical tests not changing under an affine change of the coordinate system are considered in the multivariate analysis. In the case of a multivariate linear model and a model using the canonical correlation analysis, these tests are functions of eigenvalues of matrices following a Wishart distribution. In this paper we prove the monotonicity property of test power functions being functions of elementary symmetric polynomials of eigenvalues of a matrix following a non-central Wishart distribution.