Abstract
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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 50-65 |
| Number of pages | 16 |
| Journal | Computational Statistics & Data Analysis |
| Volume | 131 |
| DOIs | |
| State | Published - Apr 7 2018 |
Bibliographical note
KAUST Repository Item: Exported on 2020-10-01Acknowledgements: 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.