The methodological contribution in this paper is motivated by biomechanical studies where data characterizing human movement are waveform curves representing joint measures such as flexion angles, velocity, acceleration, and so on. In many cases the aim consists of detecting differences in gait patterns when several independent samples of subjects walk or run under different conditions (repeated measures). Classic kinematic studies often analyse discrete summaries of the sample curves discarding important information and providing biased results. As the sample data are obviously curves, a Functional Data Analysis approach is proposed to solve the problem of testing the equality of the mean curves of a functional variable observed on several independent groups under different treatments or time periods. A novel approach for Functional Analysis of Variance (FANOVA) for repeated measures that takes into account the complete curves is introduced. By assuming a basis expansion for each sample curve, two-way FANOVA problem is reduced to Multivariate ANOVA for the multivariate response of basis coefficients. Then, two different approaches for MANOVA with repeated measures are considered. Besides, an extensive simulation study is developed to check their performance. Finally, two applications with gait data are developed.

翻译：本文的方法论贡献源于生物力学研究，该类研究将表征人体运动的数据表示为波形曲线，这些曲线代表关节的弯曲角度、速度、加速度等测量指标。在许多案例中，研究目标旨在检测当受试者在不同条件（重复测量）下行走或跑步时，多个独立样本之间的步态模式差异。经典的运动学分析通常只对样本曲线的离散汇总值进行分析，这不仅丢弃了重要信息，还可能导致有偏结果。由于样本数据本质上是曲线，本文提出采用函数数据分析方法来解决在多个独立组别于不同处理或时间段下观测到的函数变量均值曲线的相等性检验问题。本研究提出了一种新颖的、针对重复测量的函数方差分析方法，该方法利用了完整曲线信息。通过假设每条样本曲线拥有基展开，双因素函数方差分析问题被简化为对基系数这一多变量响应进行的多变量方差分析。随后，本文考虑了两种针对重复测量的多变量方差分析方法。此外，我们通过广泛的模拟研究来检验其性能，并最终利用步态数据进行了两项实际应用分析。