Repeated Measures Analysis for Functional Data Using Box-Type Approximation

Abstract

The repeated measures analysis for functional data is investigated. In the literature, the test statistic for the two-sample problem when data are from the same subject is considered. Unfortunately, the known permutation and bootstrap approximations for distribution of it may be time-consuming. To avoid this drawback, a Box-type approximation for asymptotic null distribution of that test statistic is proposed. This approximation results in a new testing procedure, which is more efficient from a computational point of view than the known ones. Root-n consistency of the new method is also proved. Via intensive simulation studies, it is found that in terms of size control and power, the new test is comparable with the known tests. An illustrative example of the use of tests in practice is also given.

Keywords

• Box-type approximation
• χ 2 -type mixture
• functional data
• repeated measures analysis
• two-cumulant approximation
• two-sample test