A Test for Two-Sample Repeated Measures Designs: Effect of High-Dimensional Data

Abstract

Problem statement: High-dimensional repeated measures data are increasingly encountered in various areas of modern science since classical multivariate statistics, e.g,. Hotelling’s T², are not well defined in the case of high-dimensional data. Approach: In this study, the test statistics with no specific form of covariance matrix for analyzing high-dimensional two-sample repeated measures designs with common equal covariance are proposed. The asymptotic distributions of the proposed test statistics also were derived. Results: A simulation study exposes the approximated Type I errors in the null case very well even though the number of subjects of each sample as small as 10. Numerical simulations study indicates that the proposed test have good power. Application of the new tests is demonstrated using data from the body-weight of male Wistar rats example. Conclusion: The proposed test statistics have an asymptotically distributed as standard normal distributions, under the null hypothesis. Simulation studies show that these test statistics still accurately control Type I error and have quite good power for any the covariance matrix pattern considered.