Directional Outlyingness for Multivariate Functional Data

• Activity Number: 220 - Robust Multivariate and High-Dimensional Analysis Using Functional Data Ranking
• Type: Topic Contributed
• Date/Time: Monday, July 31, 2017 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Wenlin Dai* and Marc G. Genton
• Companies: KAUST and KAUST
• Keywords: Centrality visualization ; Directional outlyingness ; Multivariate function data ; Outlier detection ; Outlyingness decomposition

Abstract

The direction of outlyingness is crucial to describing the centrality of multivariate functional data. Motivated by this idea, we propose a new framework that combines classical depth with the direction of outlyingness. We generalise classical depth to directional outlyingness for both point-wise and functional data. We investigate theoretical properties of functional directional outlyingness and find that it naturally decomposes functional outlyingness 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 all existing methods. Weather and electrocardiogram data demonstrate the practical application of our proposed framework.