Non-asymptotic Confidence Sets for Extrinsic Means on Spheres and Projective Spaces
Statistics Theory
2016-02-15 v1 Methodology
Statistics Theory
Abstract
Confidence sets from i.i.d. data are constructed for the extrinsic mean of a probabilty measure P on spheres, real projective spaces, and complex projective spaces, as well as Grassmann manifolds, with the latter three embedded by the Veronese-Whitney embedding. When the data are sufficiently concentrated, these are projections of a ball around the corresponding Euclidean sample mean. Furthermore, these confidence sets are rate-optimal. The usefulness of this approach is illustrated for projective shape data.
Keywords
Cite
@article{arxiv.1602.04117,
title = {Non-asymptotic Confidence Sets for Extrinsic Means on Spheres and Projective Spaces},
author = {Thomas Hotz and Florian Kelma},
journal= {arXiv preprint arXiv:1602.04117},
year = {2016}
}