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Title: Directional depth and outlyingness for multivariate functional data Authors:  Wenlin Dai - KAUST (Saudi Arabia)
Marc Genton - KAUST (Saudi Arabia) [presenting]
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 generalize classical depth/outlyingness to directional depth/outlyingness in both point-wise and functional data. We investigate the affine invariance of directional functional depth and find that it naturally decomposes functional depth into two parts: a scale depth and a shape depth, 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 directional functional outlyingness. This criterion applies to both univariate and multivariate curves and simulation studies show that it outperforms existing methods. Weather and electrocardiogram data demonstrate the practical application of our proposed framework.