4 papers · 1 filter
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…
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…
A Smeary Central Limit Theorem for Manifolds with Application to High Dimensional Spheres
Benjamin Eltzner, Stephan F. Huckemann
The (CLT) central limit theorems for generalized Frechet means (data descriptors assuming values in stratified spaces, such as intrinsic means, geodesics, etc.) on manifolds from t…