A diffusion process associated with Fréchet means

Le, Huiling (2015) A diffusion process associated with Fréchet means. Annals of Applied Probability, 25 (6). pp. 3033-3046. ISSN 1050-5164

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This paper studies rescaled images, under exp−1μ, of the sample Fréchet means of i.i.d. random variables {Xk|k≥1} with Fréchet mean μ on a Rie-mannian 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−1μ(X1), this linear transformation also depends on the global Riemannian structure of the manifold

Item Type: Article
Keywords: limiting diffusion; rescaled Frechet means; weak convergence
Schools/Departments: University of Nottingham UK Campus > Faculty of Science > School of Mathematical Sciences
Identification Number: https://doi.org/10.1214/14-AAP1066
Depositing User: Le, Huiling
Date Deposited: 11 Apr 2016 07:25
Last Modified: 13 Sep 2016 12:09
URI: http://eprints.nottingham.ac.uk/id/eprint/32707

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