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A diffusion process associated with Fréchet means

Le, Huiling

Authors

HUILING LE huiling.le@nottingham.ac.uk
Professor of Probability



Abstract

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

Journal Article Type Article
Publication Date Jan 1, 2015
Journal Annals of Applied Probability
Print ISSN 1050-5164
Electronic ISSN 1050-5164
Publisher Institute of Mathematical Statistics (IMS)
Peer Reviewed Peer Reviewed
Volume 25
Issue 6
APA6 Citation Le, H. (2015). A diffusion process associated with Fréchet means. Annals of Applied Probability, 25(6), doi:10.1214/14-AAP1066
DOI https://doi.org/10.1214/14-AAP1066
Keywords limiting diffusion; rescaled Frechet means; weak convergence
Publisher URL http://projecteuclid.org/euclid.aoap/1443703768
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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