7 papers
Clustering Schemes on the Torus with Application to RNA Clashes
Henrik Wiechers, Benjamin Eltzner, Stephan F. Huckemann +1
Molecular structures of RNA molecules reconstructed from X-ray crystallography frequently contain errors. Motivated by this problem we examine clustering on a torus since RNA shape…
Diffusion Means and Heat Kernel on Manifolds
Pernille Hansen, Benjamin Eltzner, Stefan Sommer
We introduce diffusion means as location statistics on manifold data spaces. A diffusion mean is defined as the starting point of an isotropic diffusion with a given diffusivity. T…
Finite Sample Smeariness on Spheres
Benjamin Eltzner, Shayan Hundrieser, Stephan F. Huckemann
Finite Sample Smeariness (FSS) has been recently discovered. It means that the distribution of sample Fréchet means of underlying rather unsuspicious random variables can behave as…
Smeariness Begets Finite Sample Smeariness
Do Tran, Benjamin Eltzner, Stephan Huckemann
Fréchet means are indispensable for nonparametric statistics on non-Euclidean spaces. For suitable random variables, in some sense, they "sense" topological and geometric structure…
Stability of the Cut Locus and a Central Limit Theorem for Fréchet Means of Riemannian Manifolds
Benjamin Eltzner, Fernando Galaz-Garcia, Stephan F. Huckemann +1
We obtain a Central Limit Theorem for closed Riemannian manifolds, clarifying along the way the geometric meaning of some of the hypotheses in Bhattacharya and Lin's Omnibus Centra…
Geometrical Smeariness -- A new Phenomenon of Fréchet Means
Benjamin Eltzner
In the past decades, the central limit theorem (CLT) has been generalized to non-Euclidean data spaces. Some years ago, it was found that for some random variables on the circle, t…