Approximation of the non-null distribution of generalized T2-statistics Original Research Article

The non-null distributions of Hotellingʹs T2-statistic and a generalized F-statistic [Biometrics 52 (1996) 964] are approximated by asymptotic normal distributions. The distributions are derived under assumption of ellipticity of the population from where results for the normal population also follow. The main term of the bias of Hotellingʹs T2-statistic is found in the case of normal population. A simulation experiment is carried out and its results presented. In Appendix A, derivatives of a rectangular matrix of eigenvectors of a symmetric matrix and corresponding eigevalue matrix are found.