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.

中文翻译：

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有关功能数据重复度量分析的说明

本文考虑了功能数据的重复测量分析。针对该问题的已知测试程序基于测试统计量，该统计量是样本均值函数之间的差异的整数，仅考虑“组间变异性”。我们修改此测试统计信息，以也使用有关“组内变异性”的信息。更准确地说，我们构造了新的检验统计量，该检验统计量是通过调整经典配对t得到的积分和逐点检验统计量的最大值对功能数据框架进行测试统计。测试程序基于不同的近似测试统计量零分布的方法，即Box型近似，非参数和参数自举和置换方法。这些近似值在模拟实验中确定的有限样本下表现不佳，表明是最佳的新测试。仿真和对死亡率数据的应用表明，在尺寸控制和功率方面，某些新程序优于已知测试。