This paper is motivated by medical studies in which the same patients with multiple sclerosis are examined at several successive visits and described by fractional anisotropy tract profiles, which can be represented as functions. Since the observations for each patient are dependent random processes, they follow a repeated measures design for functional data. To compare the results for different visits, we thus consider functional repeated measures analysis of variance. For this purpose, a pointwise test statistic is constructed by adapting the classical test statistic for one-way repeated measures analysis of variance to the functional data framework. By integrating and taking the supremum of the pointwise test statistic, we create two global test statistics. Apart from verifying the general null hypothesis on the equality of mean functions corresponding to different objects, we also propose a simple method for post hoc analysis. We illustrate the finite sample properties of permutation and bootstrap testing procedures in an extensive simulation study. Finally, we analyze a motivating real data example in detail.

翻译：本文源于一项医学研究，其中多发性硬化症患者在连续多次随访检查中通过分数各向异性纤维束剖面进行描述，该剖面可表示为函数形式。由于每位患者的观测值构成相依随机过程，其遵循函数型数据的重复测量设计。为比较不同随访次数的结果，我们提出函数型重复测量方差分析方法。为此，通过将经典的单因素重复测量方差分析检验统计量适配至函数型数据框架，构建了点态检验统计量。通过对点态检验统计量进行积分与取上确界，我们建立了两个全局检验统计量。除验证关于不同对象均值函数相等的原假设外，我们还提出了一种简单的后续分析方法。通过大量模拟研究，我们展示了置换检验和自助法检验过程的有限样本性质。最后，我们对一个具有启发性的实际数据案例进行了详细分析。