Statistics on Riemannian manifolds: asymptotic distribution and curvature

Abstract

In this article a nonsingular asymptotic distribution is derived for a broad class of underlying distributions on a Riemannian manifold in relation to its curvature. Also, the asymptotic dispersion is explicitly related to curvature. These results are applied and further strengthened for the planar shape space of k-ads. © 2008 American Mathematical Society.