Open Access
February 2007 Asymptotic data analysis on manifolds
Harrie Hendriks, Zinoviy Landsman
Ann. Statist. 35(1): 109-131 (February 2007). DOI: 10.1214/009053606000000993


Given an m-dimensional compact submanifold M of Euclidean space Rs, the concept of mean location of a distribution, related to mean or expected vector, is generalized to more general Rs-valued functionals including median location, which is derived from the spatial median. The asymptotic statistical inference for general functionals of distributions on such submanifolds is elaborated. Convergence properties are studied in relation to the behavior of the underlying distributions with respect to the cutlocus. An application is given in the context of independent, but not identically distributed, samples, in particular, to a multisample setup.


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Harrie Hendriks. Zinoviy Landsman. "Asymptotic data analysis on manifolds." Ann. Statist. 35 (1) 109 - 131, February 2007.


Published: February 2007
First available in Project Euclid: 6 June 2007

zbMATH: 1114.62064
MathSciNet: MR2332271
Digital Object Identifier: 10.1214/009053606000000993

Primary: 62H11
Secondary: 53A07 , 62G10 , 62G15

Keywords: Compact submanifold of Euclidean space , confidence region , cutlocus , mean location , median location , multivariate Lindeberg condition , spatial median , sphere , spherical distribution , stabilization , Stiefel manifold , Weingarten mapping

Rights: Copyright © 2007 Institute of Mathematical Statistics

Vol.35 • No. 1 • February 2007
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