A Test for One-sample Repeated Measures Designs: Effect of High-dimensional Data

High-dimensional data, the dimension p of repeated measurements per subject larger than the number n of subjects, are increasingly encountered in various areas of modern science. A test statistic for analyzing high-dimensional one-sample repeated measure designs with no specific form of variance-covariance matrix assumed is proposed. This test statistic asymptotically follows a standard normal distribution for any high dimensional data. Monte Carlo study showed that the proposed test has good power and maintain approximately the nominal level with small n and any large p. Applying the proposed test to the data from body-weight of Wistar rats example with n = 10, p = 22 is demonstrated.