TY - JOUR
T1 - Directional outlyingness for multivariate functional data
AU - Dai, Wenlin
AU - Genton, Marc G.
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: This research was supported by King Abdullah University of Science and Technology (KAUST) . The authors thank the editor, an associate editor, and three anonymous referees for their valuable comments.
PY - 2018/4/7
Y1 - 2018/4/7
N2 - The direction of outlyingness is crucial to describing the centrality of multivariate functional data. Motivated by this idea, classical depth is generalized to directional outlyingness for functional data. Theoretical properties of functional directional outlyingness are investigated and the total outlyingness can be naturally decomposed into two parts: magnitude outlyingness and shape outlyingness which represent the centrality of a curve for magnitude and shape, respectively. This decomposition serves as a visualization tool for the centrality of curves. Furthermore, an outlier detection procedure is proposed based on functional directional outlyingness. This criterion applies to both univariate and multivariate curves and simulation studies show that it outperforms competing methods. Weather and electrocardiogram data demonstrate the practical application of our proposed framework.
AB - The direction of outlyingness is crucial to describing the centrality of multivariate functional data. Motivated by this idea, classical depth is generalized to directional outlyingness for functional data. Theoretical properties of functional directional outlyingness are investigated and the total outlyingness can be naturally decomposed into two parts: magnitude outlyingness and shape outlyingness which represent the centrality of a curve for magnitude and shape, respectively. This decomposition serves as a visualization tool for the centrality of curves. Furthermore, an outlier detection procedure is proposed based on functional directional outlyingness. This criterion applies to both univariate and multivariate curves and simulation studies show that it outperforms competing methods. Weather and electrocardiogram data demonstrate the practical application of our proposed framework.
UR - http://hdl.handle.net/10754/626485
UR - http://arxiv.org/abs/1612.04615v4
UR - http://www.scopus.com/inward/record.url?scp=85046164295&partnerID=8YFLogxK
U2 - 10.1016/j.csda.2018.03.017
DO - 10.1016/j.csda.2018.03.017
M3 - Article
SN - 0167-9473
VL - 131
SP - 50
EP - 65
JO - Computational Statistics & Data Analysis
JF - Computational Statistics & Data Analysis
ER -