A note on repeated measures analysis for functional data

• Published in: Advances in statistical analysis : AStA : a journal of the German Statistical Society Vol. 104; no. 1; pp. 117 - 139
• Main Author: Smaga, Łukasz
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2020; Springer Nature B.V
• Subjects: Approximation; Data analysis; Econometrics; Economics; Finance; Insurance; Integrals; Management; Mathematics and Statistics; Original Paper; Permutations; Probability Theory and Stochastic Processes; Statistical methods; Statistical tests; Statistics; Statistics for Business; Test procedures; Within-subjects design; Hypothesis testing; Bootstrap; Box-type approximation; Repeated measures analysis; Permutation; Functional data analysis
• DOI: 10.1007/s10182-018-00348-8
• ISSN: 1863-8171

In this paper, the repeated measures analysis for functional data is considered. The known testing procedures for this problem are based on test statistic being the integral of the difference between sample mean functions, which takes into account only “between group variability”. We modify this test statistic to use also information about “within group variability”. More precisely, we construct the new test statistics being integral and supremum of pointwise test statistic obtained by adapting the classical paired t -test statistic to functional data framework. The testing procedures are based on different methods of approximating the null distribution of the test statistics, namely the Box-type approximation, nonparametric and parametric bootstrap and permutation approaches. These approximations do not perform equally well under finite samples, which is established in simulation experiments, indicating the best new tests. The simulations and an application to mortality data suggest that some of the new procedures outperform the known tests in terms of size control and power.