Bootstrapping Descriptors for Non-Euclidean Data

For data carrying a non-Euclidean geometric structure it is natural to perform statistics via geometric descriptors. Typical candidates are means, geodesics, or more generally, lower dimensional subspaces, which carry specific structure. Asymptotic theory for such descriptors is slowly unfolding and its application to statistical testing usually requires one more step: Assessing the distribution of such descriptors. To this end, one may use the bootstrap that has proven to be a very successful tool to extract inferential information from small samples. In this communication we review asymptotics for descriptors of manifold valued data and study a non-parametric bootstrap test that aims at a high power, also under the alternative.