Group leader: Prof. Dr. Lutz Dümbgen
Every now and then, we are looking at the foundations of stochastics. For instance, we derive new probability inequalities [1], work on exact confidence bounds or try to look at traditional methods from a new point of view [2]. Another line of research is empirical processes and nonparametric statistics, e.g. [3]. In particular, statistical inference under shape constraints is a recurring topic, e.g. [4, 5]. Roughly speaking, shape constraints on density or regression functions are an interesting alternative to simpler but sometimes too idealistic parametric models, and they are less ad hoc than quantitative smoothness assumptions or regularization approaches. A third line of research is multivariate statistics, where we propose new methods [6, 7] or algorithms [8].
Current collaborators from abroad include Jon A. Wellner (University of Washington, Seattle, USA) and Klaus Nordhausen (University of Jyväskylä, Finland).
