Presenter: Stephan Huckemann, University of Goettingen

 
Title: Some Aspects of Statistics for Data on Non-Euclidean Spaces
 
Abstract: We begin with some research questions leading to of non-Euclidean data such as a generation of synthetic fingerprints, correction of faulty RNA structure and phylogenetic descendence. This will lead us to the concept of generalized Fréchet means and some aspects of their asymptotic limiting behavior. It turns out, there is a -- to date not at all fully understood -- relationship between possible convergences rates and geometrical and topological invariants of sample spaces. Such limiting rates may also have unprecedented consequences --  called finite sample smeariness -- for a wide family of distribution, making quantile based tests inappropriate. More appropriate are suitably designed bootstrap test.