Type
ArticleKAUST Department
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) DivisionStatistics
Statistics Program
Date
2020-07-03Preprint Posting Date
2019-04-24Online Publication Date
2020-07-03Print Publication Date
2020-12Embargo End Date
2021-04-21Submitted Date
2019-12-03Permanent link to this record
http://hdl.handle.net/10754/660679
Metadata
Show full item recordAbstract
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.Citation
Yao, Z., Dai, W., & G. Genton, M. (2020). Trajectory functional boxplots. Stat, 9(1). doi:10.1002/sta4.289Sponsors
We thank Dr. Donald H. House and his group at Clemson University for sharing the ensemble hurricane generator code. The research reported in this paper was supported by King Abdullah University of Science and Technology (KAUST).Publisher
WileyJournal
StatDOI
10.1002/sta4.289arXiv
1904.10792Additional Links
https://onlinelibrary.wiley.com/doi/10.1002/sta4.289ae974a485f413a2113503eed53cd6c53
10.1002/sta4.289