Approximation of the non-null distribution of generalized \(T^2\)-statistics. (English) Zbl 1157.62327
Summary: The non-null distributions of Hotelling’s \(T^2\)-statistic and a generalized F-statistic [J. Läuter, Biometrics 52, No. 3, 964–970 (1996; Zbl 0867.62049)] are approximated by asymptotic normal distributions. The distributions are derived under the assumption of ellipticity of the population from where results for the normal population also follow. The main term of the bias of Hotelling’s \(T^2\)-statistic is found in the case of normal populations. 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 eigenvalue matrix are found.
MSC:
| 62E20 | Asymptotic distribution theory in statistics |
| 62H15 | Hypothesis testing in multivariate analysis |
Citations:
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