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Nonparametric statistics on manifolds with applications to shape spaces

Abhishek Bhattacharya and Rabi Bhattacharya

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Abstract

This article presents certain recent methodologies and some new results for the statistical analysis of probability distributions on manifolds. An important example considered in some detail here is the 2-D shape space of k-ads, comprising all configurations of k planar landmarks (k>2)-modulo translation, scaling and rotation.

Chapter information

Source
Bertrand Clarke and Subhashis Ghosal, eds., Pushing the Limits of Contemporary Statistics: Contributions in Honor of Jayanta K. Ghosh (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2008), 282-301

Dates
First available in Project Euclid: 28 April 2008

Permanent link to this document
https://projecteuclid.org/euclid.imsc/1209398475

Digital Object Identifier
doi:10.1214/074921708000000200

Mathematical Reviews number (MathSciNet)
MR2459231

Zentralblatt MATH identifier
1371.62001

Subjects
Primary: 62G20: Asymptotic properties
Secondary: 62E20: Asymptotic distribution theory 62H35: Image analysis

Keywords
extrinsic and intrinsic means and variations Kendall’s shape spaces two-sample nonparametric tests

Rights
Copyright © 2008, Institute of Mathematical Statistics

Citation

Bhattacharya, Abhishek; Bhattacharya, Rabi. Nonparametric statistics on manifolds with applications to shape spaces. Pushing the Limits of Contemporary Statistics: Contributions in Honor of Jayanta K. Ghosh, 282--301, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2008. doi:10.1214/074921708000000200. https://projecteuclid.org/euclid.imsc/1209398475


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References

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