Large sample theory of intrinsic and extrinsic sample means on manifolds--II

Details Large sample theory of intrinsic and extrinsic sample means on manifolds--II Large sample theory of intrinsic and extrinsic sample means on manifolds--II

2005-07-21

arxiv.org/abs/math/0507423v1

Annals of Statistics 2005, Vol. 33, No. 3, 1225-1259

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053605000000093 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053605000000093

This article develops nonparametric inference procedures for estimation and testing problems for means on manifolds. A central limit theorem for Frechet sample means is derived leading to an asymptotic distribution theory of intrinsic sample means on Riemannian manifolds. Central limit theorems are also obtained for extrinsic sample means w.r.t. an arbitrary embedding of a differentiable manifold in a Euclidean space. Bootstrap methods particularly suitable for these problems are presented. Applications are given to distributions on the sphere S^d (directional spaces), real projective space RP^{N-1} (axial spaces), complex projective space CP^{k-2} (planar shape spaces) w.r.t. Veronese-Whitney embeddings and a three-dimensional shape space \Sigma_3^4.

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