Nonparametic estimation of location and dispersion on Riemannian manifolds

Rabi Bhattacharya; Vic Patrangenaru

doi:10.1016/S0378-3758(02)00268-9

Nonparametic estimation of location and dispersion on Riemannian manifolds

Rabi Bhattacharya, Vic Patrangenaru

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

63 Scopus citations

Abstract

A central limit theorem for intrinsic means on a complete flat manifold and some asymptotic properties of the intrinsic total sample variance on an arbitrary complete manifold are given. A studentized pivotal statistic and its bootstrap analogue which yield confidence regions for the intrinsic mean on a complete flat manifold are also derived.

Original language	English (US)
Pages (from-to)	23-35
Number of pages	13
Journal	Journal of Statistical Planning and Inference
Volume	108
Issue number	1-2
DOIs	https://doi.org/10.1016/S0378-3758(02)00268-9
State	Published - Nov 1 2002
Externally published	Yes

Keywords

Bootstrapping
Consistency
Extrinsic mean
Intrinsic mean
Total intrinsic variance

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty
Applied Mathematics

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10.1016/S0378-3758(02)00268-9

Cite this

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title = "Nonparametic estimation of location and dispersion on Riemannian manifolds",

abstract = "A central limit theorem for intrinsic means on a complete flat manifold and some asymptotic properties of the intrinsic total sample variance on an arbitrary complete manifold are given. A studentized pivotal statistic and its bootstrap analogue which yield confidence regions for the intrinsic mean on a complete flat manifold are also derived.",

keywords = "Bootstrapping, Consistency, Extrinsic mean, Intrinsic mean, Total intrinsic variance",

author = "Rabi Bhattacharya and Vic Patrangenaru",

year = "2002",

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AU - Patrangenaru, Vic

PY - 2002/11/1

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AB - A central limit theorem for intrinsic means on a complete flat manifold and some asymptotic properties of the intrinsic total sample variance on an arbitrary complete manifold are given. A studentized pivotal statistic and its bootstrap analogue which yield confidence regions for the intrinsic mean on a complete flat manifold are also derived.

KW - Bootstrapping

KW - Consistency

KW - Extrinsic mean

KW - Intrinsic mean

KW - Total intrinsic variance

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Nonparametic estimation of location and dispersion on Riemannian manifolds

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

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