Large sample theory of intrinsic and extrinsic sample means on manifolds. I

• 成果类型: Article
• 署名作者: Bhattacharya, R; Patrangenaru, V
• 署名单位: Indiana University System; Indiana University Bloomington; University System of Georgia; Georgia State University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 2003
• 页码: 1-29
• 关键词: shape; probability; Consistency

摘要

Sufficient conditions are given for the uniqueness of intrinsic and extrinsic means as measures of location of probability measures Q on Riemannian manifolds. It is shown that, when uniquely defined, these are estimated consistently by the corresponding indices of the empirical (Q) over cap (n). Asymptotic distributions of extrinsic sample means are derived. Explicit computations of these indices of (Q) over cap (n) and their asymptotic dispersions are carried out for distributions on the sphere S-d (directional spaces), real projective space RPN-1 (axial spaces) and CPk-2 (planar shape spaces).