With the development of data‐monitoring techniques in various fields of science, multivariate functional data are often observed. Consequently, an increasing number of methods have appeared to extend the general summary statistics of multivariate functional data. However, trajectory functional data, as an important subtype, have not been studied very well. This article proposes two informative exploratory tools: the trajectory functional boxplot and the modified simplicial band depth (MSBD) versus wiggliness of directional outlyingness (WO) plot, to visualize the centrality of trajectory functional data. The newly defined WO index effectively measures the shape variation of curves and hence serves as a detector for shape outliers; additionally, MSBD provides a centre‐outward ranking and works as a detector for magnitude outliers. Using these two measures, the functional boxplot of the trajectory reveals centre‐outward patterns and potential outliers using the raw curves, whereas the MSBD‐WO plot illustrates such patterns and outliers in a space spanned by MSBD and WO. The proposed methods are validated on hurricane path data and migration trace data recorded from two types of birds.

中文翻译：

---

轨迹功能箱线图

随着科学各个领域数据监控技术的发展，经常会观察到多元功能数据。因此，越来越多的方法似乎扩展了多元函数数据的一般摘要统计量。但是，作为重要子类型的轨迹功能数据尚未得到很好的研究。本文提出了两种有用的探索性工具：轨迹功能箱图和修正的单纯形谱带深度（MSBD）与定向偏向性（WO）图的摆动性，以可视化轨迹功能数据的中心性。新定义的WO指数可有效测量曲线的形状变化，因此可作为形状异常值的检测器；此外，MSBD还提供了中心向外的排名，并可以作为幅度异常值的检测器。使用这两个度量，轨迹的功能箱图使用原始曲线揭示了中心向外的模式和潜在的离群值，而MSBD-WO图则说明了由MSBD和WO跨越的空间中的这些模式和离群值。所提出的方法在飓风路径数据和记录自两种鸟类的迁徙跟踪数据上得到了验证。