Directional Outlyingness for Multivariate Functional Data

Abstract

The direction of outlyingness is crucial to describing the centrality of multivariate functional data. Motivated by this idea, we generalize classical depth to directional outlyingness for functional data. We investigate theoretical properties of functional directional outlyingness and find that 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. Using this decomposition, we provide a visualization tool for the centrality of curves. Furthermore, we design an outlier detection procedure 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.

36 pages, 7 figures, Computational Statistics & Data Analysis, 2018

References in corpus (3)

• Detecting and handling outlying trajectories in irregularly sampled functional datasets
• A Study of Functional Depths
• Total Variation Depth for Functional Data

Cited by in corpus (9)

• scikit-fda: A Python Package for Functional Data Analysis
• Elastic depths for detecting shape anomalies in functional data
• A Visual Analytics Approach for Hardware System Monitoring with Streaming Functional Data Analysis
• Sparse Functional Boxplots for Multivariate Curves
• Detecting and Classifying Outliers in Big Functional Data
• Functional outlier detection for density-valued data with application to robustify distribution to distribution regression
• Theory of high-dimensional outliers
• Outlier Detection for Functional Data with R Package fdaoutlier
• Trajectory Functional Boxplots