Barycenters and ANOVA for Point Pattern Data
von Raoul Müller
Datum der mündl. Prüfung:2022-04-29
Betreuer:Prof. Dr. Dominic Schuhmacher
Gutachter:Prof. Dr. Dominic Schuhmacher
Gutachter:Prof. Dr. Anita Schöbel
EnglischIn this thesis a new metric for point patterns is developed. A heuristic algorithm is presented, that computes barycenters with respect to the new metric. The barycenters are then used in ANOVA procedures, to assess the differences between groups of point patterns. Additionally, a new statistical test is introduced, that depends solely on the pairwise distances between the observations. The last topic in this thesis is the barycenter computation of a set of points in a Euclidean space. This problem arises as a subproblem of the barycenter calculation of point patterns and is moreover a generalization of the problem introduced by Pierre de Fermat.
Keywords: point pattern; ANOVA; barycenter; Levene's test