An angle-based multivariate functional pseudo-depth for shape outlier detection

A measure especially designed for detecting shape outliers in functional data is presented. It is based on the tangential angles of the intersections of the centred data and can be interpreted like a data depth. Due to its theoretical properties we call it functional tangential angle (FUNTA) pseudo-depth. Furthermore we introduce a robustification (rFUNTA). The existence of intersection angles is ensured through the centring. Assuming that shape outliers in functional data follow a different pattern, the distribution of intersection angles differs. Furthermore we formulate a population version of FUNTA in the context of Gaussian processes. We determine sample breakdown points of FUNTA and compare its performance with respect to outlier detection in simulation studies and a real data example.