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Limit theorems for empirical Fréchet means of independent and non-identically distributed manifold-valued random variables

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Kendall, Wilfrid S. and Le, Huiling. (2011) Limit theorems for empirical Fréchet means of independent and non-identically distributed manifold-valued random variables. Brazilian Journal of Probability and Statistics, Vol.25 (No.3). pp. 323-352. ISSN 0103-0752

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Official URL: http://dx.doi.org/10.1214/11-BJPS141

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 vector-valued random variables, which may be of independent interest and is therefore the subject of a self-contained section. This vector-valued 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:	0103-0752
Date:	2011
Volume:	Vol.25
Number:	No.3
Page Range:	pp. 323-352
Identification Number:	10.1214/11-BJPS141
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
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URI:	http://wrap.warwick.ac.uk/id/eprint/37637