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

• 成果类型: Article
• 署名作者: Bhattacharya, R; Patrangenaru, V
• 署名单位: University of Arizona; Texas Tech University System; Texas Tech University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053605000000093
• 发表日期: 2005
• 页码: 1225-1259
• 关键词: shape; bootstrap; location; image

摘要

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 Sal (directional spaces), real projective space Rp(N-1) (axial spaces), complex projective space Cpk-2 (planar shape spaces) w.r.t. Veronese-Whitney embeddings and a threedimensional shape space Sigma(4)(3).