A DIFFUSION PROCESS ASSOCIATED WITH FRECHET MEANS

• 成果类型: Article
• 署名作者: Le, Huiling
• 署名单位: University of Nottingham
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/14-AAP1066
• 发表日期: 2015
• 页码: 3033-3046
• 关键词: extrinsic sample means; MANIFOLDS

摘要

This paper studies rescaled images, under exp(mu)(-1) of the sample Frechet means of i.i.d. random variables {X-k vertical bar k >= 1} with Frechet mean mu on a Riemannian manifold. We show that, with appropriate scaling, these images converge weakly to a diffusion process. Similar to the Euclidean case, this limiting diffusion is a Brownian motion up to a linear transformation. However, in addition to the covariance structure of exp(mu)(-1) (X-1), this linear transformation also depends on the global Riemannian structure of the manifold.