Power function of statistical tests dependent on elementary symmetric polynomials} / P. A. Kashitsyn. //Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2012. № 3. P. 55-58 [Moscow Univ. Math. Bulletin. Vol. 67, N 3, 2012.].
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.
Key words: multivariate analysis, power function, elementary symmetric polynomial, Wishart distribution.