ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

12. Probability and Statistics

1991 MS Classification: 62 Glimm, Ekkehard, Universität Magdeburg, Germany Power and admissibility of spherical multivariate tests In 1996, Läuter proposed a class of new exact level-α tests for multivariate, normally distributed data X. These tests are alternatives to classical MANOVA tests (e. g. Hotelling’s T^{2}). They overcome the limitations of the classical methods concerning sample size and dimension. Under certain conditions, spherical tests are much more powerful than their classical counterparts. To construct a spherical test for a specific linear hypothesis, a coefficient vector d has to be defined as a function of a corresponding sums-of-products matrix G_{xx}. It can be shown by a Bayesian approach that the largest eigenvector of G_{xx}d =Diag (G_{xx}) dλ provides an admissible test within this settting. Reference: J. Läuter, E. Glimm, and S. Kropf (1997): Multivariate tests based on left-spherically distributed linear scores. Submitted to The Annals of Statistics.