The Library
Limit theorems for empirical Fréchet means of independent and non-identically distributed manifold-valued random variables
Tools
Kendall, W. 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. doi:10.1214/11-BJPS141 ISSN 0103-0752.
|
PDF
WRAP_Kendall_KendallLe-2011.pdf - Published Version - Requires a PDF viewer. Download (279Kb) |
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, Engineering and Medicine > 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 | ||||
Official Date: | 2011 | ||||
Dates: |
|
||||
Volume: | Vol.25 | ||||
Number: | No.3 | ||||
Page Range: | pp. 323-352 | ||||
DOI: | 10.1214/11-BJPS141 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Date of first compliant deposit: | 1 August 2016 | ||||
Date of first compliant Open Access: | 1 August 2016 |
Data sourced from Thomson Reuters' Web of Knowledge
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |
Downloads
Downloads per month over past year