Intrinsic means on the circle: uniqueness, locus and asymptotics

DOI10.1007/s10463-013-0444-7zbMath1331.62269arXiv1108.2141OpenAlexW2027729304MaRDI QIDQ2255171

Thomas Hotz, Stephan F. Huckemann

Publication date: 6 February 2015

Published in: Annals of the Institute of Statistical Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1108.2141

zbMATH Keywords

asymptotic normalityconvergence ratecentral limit theoremdirectional statisticscircular statisticsintrinsic mean

Mathematics Subject Classification ID

Directional data; spatial statistics (62H11) Central limit and other weak theorems (60F05)

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Cites Work

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• Intrinsic statistics on Riemannian manifolds: Basic tools for geometric measurements
• The Karcher mean of a class of symmetric distributions on the circle
• Large sample theory of intrinsic and extrinsic sample means on manifolds. I
• Large sample theory of intrinsic and extrinsic sample means on manifolds. II.
• Directions and projective shapes
• Inference on 3D Procrustes Means: Tree Bole Growth, Rank Deficient Diffusion Tensors and Perturbation Models
• Riemannian $L^{p}$ center of mass: Existence, uniqueness, and convexity
• Statistical Analysis of Circular Data
• Riemannian center of mass and mollifier smoothing
• On the consistency of procrustean mean shapes
• Direction Estimation by Minimum Squared Arc Length

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