Stability of the Cut Locus and a Central Limit Theorem for Fréchet Means of Riemannian Manifolds
2021 | journal article. A publication with affiliation to the University of Göttingen.
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Stability of the Cut Locus and a Central Limit Theorem for Fréchet Means of Riemannian Manifolds
Eltzner, B. ; Galaz-García, F.; Huckemann, S. F. & Tuschmann, W. (2021)
Proceedings of the American Mathematical Society, 149(09) pp. 3947-3963. DOI: https://doi.org/10.1090/proc/15429
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Details
- Authors
- Eltzner, Benjamin ; Galaz-García, Fernando; Huckemann, Stephan F. ; Tuschmann, Wilderich
- Abstract
- We obtain a Central Limit Theorem for closed Riemannian manifolds, clarifying along the way the geometric meaning of some of the hypotheses in Bhattacharya and Lin's Omnibus Central Limit Theorem for Fr'echet means. We obtain our CLT assuming certain stability hypothesis for the cut locus, which always holds when the manifold is compact but may not be satisfied in the non-compact case.
- Issue Date
- 2021
- Journal
- Proceedings of the American Mathematical Society
- Project
- RTG 2088: Research Training Group 2088 Discovering structure in complex data: Statistics meets Optimization and Inverse Problems
- ISSN
- 0002-9939
- eISSN
- 1088-6826
- Language
- English
