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Limit theorems for empirical Fréchet means of independent and nonidentically distributed manifoldvalued random variables
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Kendall, Wilfrid S. and Le, Huiling. (2011) Limit theorems for empirical Fréchet means of independent and nonidentically distributed manifoldvalued random variables. Brazilian Journal of Probability and Statistics, Vol.25 (No.3). pp. 323352. ISSN 01030752

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Official URL: http://dx.doi.org/10.1214/11BJPS141
Abstract
We prove weak laws of large numbers and central limit theorems
of Lindeberg type for empirical centres of mass (empirical Fréchet means)
of independent nonidentically distributed random variables taking values in
Riemannian manifolds. In order to prove these theorems we describe and
prove a simple kind of Lindeberg–Feller central approximation theorem for
vectorvalued random variables, which may be of independent interest and
is therefore the subject of a selfcontained section. This vectorvalued result
allows us to clarify the number of conditions required for the central limit
theorem for empirical Fréchet means, while extending its scope.
Item Type:  Journal Article  

Subjects:  Q Science > QA Mathematics  
Divisions:  Faculty of Science > Statistics  
Library of Congress Subject Headings (LCSH):  Geometry, Riemannian, Limit theorems (Probability theory), Random variables  
Journal or Publication Title:  Brazilian Journal of Probability and Statistics  
Publisher:  Duke University Press  
ISSN:  01030752  
Official Date:  2011  
Dates: 


Volume:  Vol.25  
Number:  No.3  
Page Range:  pp. 323352  
Identifier:  10.1214/11BJPS141  
Status:  Peer Reviewed  
Publication Status:  Published  
Access rights to Published version:  Restricted or Subscription Access  
References:  Afsari, B. (2011). Riemannian Lp center of mass: Existence, uniqueness, and convexity. Proc. Amer. 

URI:  http://wrap.warwick.ac.uk/id/eprint/37637 
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