A note on repeated measures analysis for functional data

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 tes...

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Bibliographic Details
Published in:Advances in statistical analysis : AStA : a journal of the German Statistical Society 2020-03, Vol.104 (1), p.117-139
Main Author: Smaga, Łukasz
Format: Article
Language:English
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
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Summary: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.
ISSN:1863-8171
1863-818X
DOI:10.1007/s10182-018-00348-8