Limit theorems for empirical Fréchet means of independent and non-identically distributed manifold-valued random variables

DOI10.1214/11-BJPS141zbMath1234.60025arXiv1102.0228MaRDI QIDQ642198

Wilfrid S. Kendall, Huiling Le

Publication date: 25 October 2011

Published in: Brazilian Journal of Probability and Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1102.0228

zbMATH Keywords

Newton's methodKähler manifoldcurvatureHessianexponential mapgradientcentral limit theoremweak law of large numbersLindeberg conditionFréchet meancentral approximation theoremempirical Fréchet meanRiemannian centre of mass

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05)

Related Items (20)

Symmetry tests for manifold-valued random variables ⋮ Convergence rates for empirical barycenters in metric spaces: curvature, convexity and extendable geodesics ⋮ Mean shapes, projections and intrinsic limiting distributions ⋮ Rejoinder to the discussion ⋮ Sets that maximize probability and a related variational problem ⋮ A diffusion process associated with Fréchet means ⋮ Limiting behaviour of Fréchet means in the space of phylogenetic trees ⋮ Fast convergence of empirical barycenters in Alexandrov spaces and the Wasserstein space ⋮ Geometry of sample spaces ⋮ Spatial quantiles on the hypersphere ⋮ Differential Geometry for Model Independent Analysis of Images and Other Non-Euclidean Data: Recent Developments ⋮ Statistical Methods Generalizing Principal Component Analysis to Non-Euclidean Spaces ⋮ Fréchet means and Procrustes analysis in Wasserstein space ⋮ Flexible non-parametric regression models for compositional data ⋮ Intrinsic Riemannian functional data analysis ⋮ Recursive Computation of the Fréchet Mean on Non-positively Curved Riemannian Manifolds with Applications ⋮ Principal Flows ⋮ Omnibus CLTs for Fréchet means and nonparametric inference on non-Euclidean spaces ⋮ Nonparametric analysis of non-Euclidean data on shapes and images ⋮ On the measure of the cut locus of a Fréchet mean

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