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Februrary 2003 Large sample theory of intrinsic and extrinsic sample means on manifolds
Rabi Bhattacharya, Vic Patrangenaru
Ann. Statist. 31(1): 1-29 (Februrary 2003). DOI: 10.1214/aos/1046294456

Abstract

Sufficient conditions are given for the uniqueness of intrinsic and extrinsic means as measures of location of probability measures Q on Riemannian manifolds. It is shown that, when uniquely defined, these are estimated consistently by the corresponding indices of the empirical $\hat Q_n$. Asymptotic distributions of extrinsic sample means are derived. Explicit computations of these indices of $\hat Q_n$ and their asymptotic dispersions are carried out for distributions on the sphere $S^d$ (directional spaces), real projective space $\mathbb{R}P^{N-1}$ (axialspaces) and $\mathbb{C} P^{k-2}$ (planar shape spaces).

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Rabi Bhattacharya. Vic Patrangenaru. "Large sample theory of intrinsic and extrinsic sample means on manifolds." Ann. Statist. 31 (1) 1 - 29, Februrary 2003. https://doi.org/10.1214/aos/1046294456

Information

Published: Februrary 2003
First available in Project Euclid: 26 February 2003

zbMATH: 1020.62026
MathSciNet: MR1962498
Digital Object Identifier: 10.1214/aos/1046294456

Subjects:
Primary: 62H11
Secondary: 62H10

Keywords: consistency , equivariant embedding , extrinsic mean , Fréchet mean , intrinsic mean , mean planar shape

Rights: Copyright © 2003 Institute of Mathematical Statistics

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Vol.31 • No. 1 • Februrary 2003
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