A1615
Title: Area-based epigraph and hypograph indices as a tool to detect outliers in functional data
Authors: Belen Pulido Bravo - Universidad Carlos III de Madrid (Spain) [presenting]
Rosa Lillo - Universidad Carlos III de Madrid (Spain)
Alba Franco-Pereira - Universidad Complutense de Madrid (Spain)
Abstract: The epigraph and hypograph indices offer alternative methods to functional depth when the goal is to order functions. Unlike functional depth, which provides a center-outward ranking, these indices produce top-to-bottom or bottom-to-top orderings. Modified versions of these indices, called ABEI and ABHI, are introduced based on the areas between curves. These new indices are considered here for detecting outliers in functional data. The primary advantage of ABEI and ABHI over their original formulations is their enhanced ability to isolate outliers more effectively. Furthermore, a novel procedure for outlier detection in functional data is proposed, utilizing ABEI and ABHI applied to the data as well as its first and second derivatives. This transforms the functional dataset into a multivariate one, enabling the application of established multivariate outlier detection techniques. The introduced approach is validated through extensive experimentation on both simulated and real-world datasets, demonstrating its competitive performance compared to existing methods in functional data analysis.
