Multivariate functional data are becoming ubiquitous with advances in modern technology and are substantially more complex than univariate functional data. We propose and study a novel model for multivariate functional data where the component processes are subject to mutual time warping. That is, the component processes exhibit a similar shape but are subject to systematic phase variation across their time domains. To address this previously unconsidered mode of warping, we propose new registration methodology that is based on a shift-warping model. Our method differs from all existing registration methods for functional data in a fundamental way. Namely, instead of focusing on the traditional approach to warping, where one aims to recover individual-specific registration, we focus on shift registration across the components of a multivariate functional data vector on a population-wide level. Our proposed estimates for these shifts are identifiable, enjoy parametric rates of convergence, and often have intuitive physical interpretations, all in contrast to traditional curve-specific registration approaches. We demonstrate the implementation and interpretation of the proposed method by applying our methodology to the Zürich Longitudinal Growth data and study its finite sample properties in simulations.

中文翻译：

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多元功能数据的跨组件配准，适用于生长曲线

随着现代技术的进步，多元函数数据变得无处不在，并且比单变量函数数据复杂得多。我们提出并研究了一种用于多元功能数据的新模型，其中组件过程受到相互时间扭曲。也就是说，组件过程表现出相似的形状，但在其时域中会受到系统相位变化的影响。为了解决这种以前未考虑的翘曲模式，我们提出了基于移位翘曲模型的新配准方法。我们的方法在根本上不同于所有现有的功能数据注册方法。也就是说，不是专注于传统的翘曲方法，一种旨在恢复个人特定注册的方法，我们专注于在人群范围内跨多元功能数据向量的组件的移位配准。我们对这些变化的建议估计是可识别的，享受参数收敛速度，并且通常具有直观的物理解释，这与传统的特定于曲线的配准方法形成鲜明对比。我们通过将我们的方法应用于苏黎世纵向增长数据并在模拟中研究其有限样本属性来演示所提出方法的实施和解释。