A test for repeated measurements designs with high dimensional data

Abstract

Repeated measurements across time on the same subject are frequently observed in several scientific fields. A new challenge to statisticians today is dealing with conditions where the dimension of repeated measurements per subject is larger than the number of subjects, called high dimensional data. High dimensional repeated measurements data are increasingly encountered in various areas of modern science because classical multivariate statistics are not well defined. In this dissertation, test statistics for analyzing high dimensional one- and twosample repeated measurements designs are proposed. The test statistics do not depend on any specific pattern of the variance-covariance matrix. The proposed test statistics asymptotically follow a standard normal distribution. Monte Carlo simulation studies showed that the proposed test statistics have good power and approximately maintain the nominal level with small and any large . Moreover, the empirical power values of the proposed test statistics and the modified ANOVA-type statistics are rather close but the proposed test statistics always had a slightly higher power than the modified ANOVA-type statistics for all cases considered in the simulation. Application of the test statistics is illustrated using real-life data from a body-weight study of male Wistar rats.