High-Dimensional Repeated Measures Under Non-Normality

• Activity Number: 232
• Type: Topic Contributed
• Date/Time: Monday, August 2, 2010 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Edgar Brunner*+ and Hans-Joachim Helms
• Companies: University of Goettingen and University of Goettingen
• Keywords: Box's \epsilon ; highdimensional repeated measures ; repeated measures designs ; Box approximation

Abstract

In repeated measures designs involving n independent subjects and d repeated measures linear hypotheses about the repeated measures are tested using quadratic forms. The number d of repeated measures is assumed to be fixed while n \to \infty. Neither a multivariate normal distribution nor a particular structure of the covariance matrix is assumed. The asymptotic distribution of the quadratic forms is approximated by a \chi^2-distribution using an approximately unbiased estimator of Box's \epsilon. This estimator is obtained from bilinear and quadratic forms which are dimensionally stable. It is then shown by simulations that the approximation by the asymptotic \chi^2-distribution is quite accurate, even for a small number of replications n=10 while d may be arbitrary.