A1131
Title: Computation of non-zero empirical expectile depths
Authors: Maicol Ochoa - Universidad Carlos III de Madrid (Spain) [presenting]
Ignacio Cascos - Universidad Carlos III de Madrid (Spain)
Ha Thi Khanh Linh - Free University of Bolzano - Bozen (Italy)
Abstract: In nonparametric multivariate statistics, the depth of a point indicates its degree of centrality relative to a data cloud. A higher depth means greater centrality. Several depth concepts, such as halfspace, simplicial, and zonoid depths, have gained popularity due to their utility in outlier detection, supervised and unsupervised classification, and process monitoring. However, the empirical versions of such depth notions assume a value of zero for any point outside the convex hull of the data cloud, which poses challenges for real-world applications. To address this limitation, the focus is on the expectile depth and introduction of related empirical constructions that remain strictly positive for any point, regardless of its position. Discussion includes the computation of these constructions in any dimension.
