The development of the spherical multivariate tests [Läuter 1996, Läuter, Glimm and Kropf 1998] has provided many possibilities of exact inference for clinical studies with multiple endpoints. The tests are applicable for the mean-value comparison of several populations with an unknown covariance matrix. They are especially suitable for cases with a high number of variables p and a small sample size n. Thus, the large dimension p can compensate for a too small sample size n to a certain extent to avoid numerical and statistical instability. In the talk, a new method of the calculation of linear principal- component scores is presented which is based only on the within-sample covariances and yields nevertheless an level-alpha test in every case. This method can be applied for the determination of exact confidence intervals of linear scores.

References:

1. Läuter, J. (1996): Exact t and F tests for analyzing studies with multiple endpoints. Biometrics 52, 964-970.
2. Läuter, J., Glimm, E., and Kropf, S. (1998): Multivariate tests based on left-spherically distributed linear scores. The Annals of Statistics 26, 1972-1988.