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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Statistics on Riemannian manifolds: asymptotic distribution and curvature


Authors: Abhishek Bhattacharya and Rabi Bhattacharya
Journal: Proc. Amer. Math. Soc. 136 (2008), 2959-2967
MSC (2000): Primary 62G20; Secondary 62E20, 62H35
Published electronically: March 14, 2008
MathSciNet review: 2399064
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Abstract: In this article a nonsingular asymptotic distribution is derived for a broad class of underlying distributions on a Riemannian manifold in relation to its curvature. Also, the asymptotic dispersion is explicitly related to curvature. These results are applied and further strengthened for the planar shape space of k-ads.


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Additional Information

Abhishek Bhattacharya
Affiliation: Department of Mathematics, University of Arizona, Tucson, Arizona 85721
Email: abhishek@math.arizona.edu

Rabi Bhattacharya
Affiliation: Department of Mathematics, University of Arizona, Tucson, Arizona 85721
Email: rabi@math.arizona.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09445-8
PII: S 0002-9939(08)09445-8
Keywords: Intrinsic mean, shape space of k-ads, nonparametric analysis
Received by editor(s): July 15, 2007
Published electronically: March 14, 2008
Additional Notes: This research was supported by NSF Grant DMS 04-06143
Communicated by: Edward C. Waymire
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.