Statistics on Riemannian manifolds: Asymptotic distribution and curvature

Abhishek Bhattacharya; Rabi Bhattacharya

doi:10.1090/S0002-9939-08-09445-8

Statistics on Riemannian manifolds: Asymptotic distribution and curvature

Abhishek Bhattacharya
, Rabi Bhattacharya

Mathematics

Research output: Contribution to journal › Article › peer-review

33 Scopus citations

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.

Original language	English (US)
Pages (from-to)	2959-2967
Number of pages	9
Journal	Proceedings of the American Mathematical Society
Volume	136
Issue number	8
DOIs	https://doi.org/10.1090/S0002-9939-08-09445-8
State	Published - Aug 2008

Keywords

Intrinsic mean
Nonparametric analysis
Shape space of k-ads

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/S0002-9939-08-09445-8

Cite this

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title = "Statistics on Riemannian manifolds: Asymptotic distribution and curvature",

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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T2 - Asymptotic distribution and curvature

AU - Bhattacharya, Abhishek

AU - Bhattacharya, Rabi

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N2 - 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.

AB - 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.

KW - Intrinsic mean

KW - Nonparametric analysis

KW - Shape space of k-ads

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Statistics on Riemannian manifolds: Asymptotic distribution and curvature

Abstract

Keywords

ASJC Scopus subject areas

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