Generalized F-tests for the multivariate normal mean

Based on Läuter’s [Läuter, J., 1996. Exact tt and FF tests for analyzing studies with multiple endpoints. Biometrics 52, 964–970] exact tt test for biometrical studies related to the multivariate normal mean, we develop a generalized FF-test for the multivariate normal mean and extend it to multiple comparison. The proposed generalized FF-tests have simple approximate null distributions. A Monte Carlo study and two real examples show that the generalized FF-test is at least as good as the optional individual Läuter’s test and can improve its performance in some situations where the projection directions for the Läuter’s test may not be suitably chosen. The generalized FF-test could be superior to individual Läuter’s tests and the classical Hotelling T2T2-test for the general purpose of testing the multivariate normal mean. It is shown by Monte Carlo studies that the extended generalized FF-test outperforms the commonly-used classical test for multiple comparison of normal means in the case of high dimension with small sample sizes.