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June 2005 Large sample theory of intrinsic and extrinsic sample means on manifolds—II
Rabi Bhattacharya, Vic Patrangenaru
Ann. Statist. 33(3): 1225-1259 (June 2005). DOI: 10.1214/009053605000000093


This article develops nonparametric inference procedures for estimation and testing problems for means on manifolds. A central limit theorem for Fréchet sample means is derived leading to an asymptotic distribution theory of intrinsic sample means on Riemannian manifolds. Central limit theorems are also obtained for extrinsic sample means w.r.t. an arbitrary embedding of a differentiable manifold in a Euclidean space. Bootstrap methods particularly suitable for these problems are presented. Applications are given to distributions on the sphere Sd (directional spaces), real projective space ℝPN−1 (axial spaces), complex projective space ℂPk−2 (planar shape spaces) w.r.t. Veronese–Whitney embeddings and a three-dimensional shape space Σ34.


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Rabi Bhattacharya. Vic Patrangenaru. "Large sample theory of intrinsic and extrinsic sample means on manifolds—II." Ann. Statist. 33 (3) 1225 - 1259, June 2005.


Published: June 2005
First available in Project Euclid: 1 July 2005

zbMATH: 1072.62033
MathSciNet: MR2195634
Digital Object Identifier: 10.1214/009053605000000093

Primary: 62H11
Secondary: 62H10

Keywords: Bootstrapping , central limit theorem , Confidence regions , extrinsic mean , Fréchet mean

Rights: Copyright © 2005 Institute of Mathematical Statistics


Vol.33 • No. 3 • June 2005
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