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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 
Volume:  Vol.25 
Number:  No.3 
Page Range:  pp. 323352 
Identification Number:  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 
Data sourced from Thomson Reuters' Web of Knowledge
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