A diffusion process associated with Fréchet means
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 d...
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| Format: | Article |
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Institute of Mathematical Statistics
2015
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| Online Access: | https://eprints.nottingham.ac.uk/32707/ |
| _version_ | 1848794472489418752 |
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| author | Le, Huiling |
| author_facet | Le, Huiling |
| author_sort | Le, Huiling |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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 |
| first_indexed | 2025-11-14T19:16:44Z |
| format | Article |
| id | nottingham-32707 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:16:44Z |
| publishDate | 2015 |
| publisher | Institute of Mathematical Statistics |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-327072020-05-04T20:11:16Z https://eprints.nottingham.ac.uk/32707/ A diffusion process associated with Fréchet means Le, Huiling 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 Institute of Mathematical Statistics 2015 Article PeerReviewed Le, Huiling (2015) A diffusion process associated with Fréchet means. Annals of Applied Probability, 25 (6). pp. 3033-3046. ISSN 1050-5164 limiting diffusion; rescaled Frechet means; weak convergence http://projecteuclid.org/euclid.aoap/1443703768 doi:10.1214/14-AAP1066 doi:10.1214/14-AAP1066 |
| spellingShingle | limiting diffusion; rescaled Frechet means; weak convergence Le, Huiling A diffusion process associated with Fréchet means |
| title | A diffusion process associated with Fréchet means |
| title_full | A diffusion process associated with Fréchet means |
| title_fullStr | A diffusion process associated with Fréchet means |
| title_full_unstemmed | A diffusion process associated with Fréchet means |
| title_short | A diffusion process associated with Fréchet means |
| title_sort | diffusion process associated with fréchet means |
| topic | limiting diffusion; rescaled Frechet means; weak convergence |
| url | https://eprints.nottingham.ac.uk/32707/ https://eprints.nottingham.ac.uk/32707/ https://eprints.nottingham.ac.uk/32707/ |