A1237
Title: Finite elements based data depths for the analysis of functional data over non-convex domains
Authors: Michele Cavazzutti - Charles University (Italy) [presenting]
Eleonora Arnone - University of Turin (Italy)
Stanislav Nagy - Charles University (Czechia)
Laura Sangalli - Politecnico di Milano (Italy)
Abstract: A covariance-sensitive depth measure for functional data observed over complex, multidimensional domains is introduced. The approach specifically addresses settings where observations are discretely and irregularly sampled, often restricted to subsets of nonconvex supports. To account for these geometric complexities, a Finite Element-based framework is proposed that relies on geometrically compliant representations of the support, such as Delaunay triangulations and Voronoi tessellations. This construction enables robust treatment of discrete measurements in multidimensional settings and naturally accommodates missingness due to partially observed domains while maintaining computational efficiency. By leveraging second-order information, the resulting depth measure captures shape and covariance variations without requiring smoothing, derivatives, or prior reconstruction. The methodology is illustrated through two distinct applications: the analysis of surface water temperature in Lake Victoria from the ARC-Lake database and the processing of neuroimaging data.
