Humboldt-Universität zu Berlin - Statistics

Prof. Greven receives funding for a second funding period (2026-2028) of project „Flexible regression methods for curve and shape data“ from the German Research Foundation (DFG). The first funding period was very successful, with 10 papers and 6 R packages resulting, as well as several awards including the Wolfgang Wetzel award of the German Statistical Association and the Gustav-Adolf Lienert award of the International Biometric Society - German Region to Almond Stöcker. 

 

Using modern imaging and tracking devices, researchers in a wide range of areas collect more and more data, where each observation corresponds to a two- or higher-dimensional curve. Examples are movement patterns and bone outlines. In some settings, these can be viewed as multivariate functional data. In others, the functional shape is primarily of interest, i.e. the equivalence class of the curve accounting for invariance to translation, rotation, scaling and/or re-parameterization along the curve. This induces a non-Euclidean geometry on the resulting quotient spaces (shape spaces).

 

The goal of this project is to advance the field of functional shape analysis both in terms of the theory and in terms of usefully applicable methods for real data analysis problems. In particular, a general and flexible additive regression framework for curves and shapes in two (or potentially higher) dimensions is developed and implemented. A focus is on allowing different combinations of invariances with respect to re-parameterization, translation, rotation and/or scaling according to the needs in a specific data scenario, flexibility in specifying various additive covariate effect types, and allowing for curves and shapes to be irregularly or sparsely sampled. In the second funding period, we will additionally look at error-prone observations, elastic functional and functional shape covariates, and elastic multivariate functional principal component analysis.