Large sample theory of intrinsic and extrinsic sample means on manifolds—II
Rabi Bhattacharya and Vic Patrangenaru
Source: Ann. Statist. Volume 33, Number 3 (2005), 1225-1259.
Abstract
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.
Primary Subjects: 62H11
Secondary Subjects: 62H10
Keywords: Fréchet mean; extrinsic mean; central limit theorem; confidence regions; bootstrapping
Full-text: Open access
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aos/1120224101
Digital Object Identifier: doi:10.1214/009053605000000093
Mathematical Reviews number (MathSciNet):
MR2195634
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