AEI-DFG STENED: Stein-based goodness-of-fit TEsts for Non-Euclidean Data

• Applicant: Dr. Bruno Ebner
• Subject Area: Mathematics
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 541565572

The ‘Stein-based goodness-of-fit TEsts for Non-Euclidean Data’ (STENED) project aims to leverage Stein’s method to create an overarching testing toolbox for parametric and semiparametric distribution models defined on the hypersphere S^d, d ≥ 1, and on the Cartesian products thereof present in skeletal representations of three-dimensional objects. Specifically, STENED aims to fulfill four main research objectives exploiting Stein’s approach: (1) develop goodness-of-fit tests for distributions on the sphere with known and unknown parameters; (2) create new tests for for rotational symmetry on S^d and construct a goodness-of-fit test for the Johnson–Wehrly distribution class on (S^1)^2; (3) construct goodness-of-fit and independence tests for practically-relevant models for skeletal representations on R^m × (S^d)^r; and (4) advance goodness-of-fit tests for high-dimensional distributions on S^d. The methodology developed in STENED will have transversal applications in the fields where directional data and skeletal representations are present, with particular emphasis in novel case studies in astronomy and medical imaging. STENED is designed to have an organic and fluent German–Spanish collaboration rooted in (1) the joint supervision of PhD theses and (2) research visits between the both countries and the collaborators of the project.

• DFG Programme: Research Grants
• International Connection: Spain
• Partner Organisation: Agencia Estatal de Investigación
• Co-Investigator: Professor Dr. Norbert Henze
• Cooperation Partner: Professor Eduardo García Portugués, Ph.D.