Title: Multivariate tests in high dimensions and unstructured dependence
Authors: Solomon Harrar - University of Kentucky (United States) [presenting]
Xiaoli Kong - University of Kentucky (United States)
Abstract: Recent results for comparison of high-dimensional mean vectors make assumptions that requires the dependence between the variables to be weak. This requirement fails to be satisfied, for example, by elliptically contoured distributions. We relax the dependence conditions that seem to be the standard assumption in high-dimensional asymptotic tests. With the relaxed condition, the scope of applicability of the the results broadens. In particular, strong mixing type of dependence and applications for rank-based comparison of groups are covered. For the rank-based methods, hypotheses are formulated in terms of meaningful and easy to interpret nonparametric measures of effect. This formulation accommodate data in binary, discrete, ordinal and continuous scales seamlessly. The problem is setup in a general and flexible form that extension of the results to general factorial design, including repeated measures, are formally illustrated. Simulation studies are used to evaluate the numerical performance of the results in practical scenarios. Data from Electroencephalograph (EEG) experiment is analyzed to illustrate the application of the results.