Student or educator? Sign up with your school email and get 6 months of Pro free.
CoChat
Sign Up
Cited by 401

The DOI matches its Crossref record; 44 of the 44 references it cites were found in a registry or an index.

Large sample theory of intrinsic and extrinsic sample means on manifolds

Open access
Bhattacharya, Rabi, Patrangenaru, Vic·2003·The Annals of Statistics
DOI 10.1214/aos/1046294456
Open this paper in CoChat — free account

Abstract

Sufficient conditions are given for the uniqueness of intrinsic and extrinsic means as measures of location of probability measures Q on Riemannian manifolds. It is shown that, when uniquely defined, these are estimated consistently by the corresponding indices of the empirical $\hat Q_n$. Asymptotic distributions of extrinsic sample means are derived. Explicit computations of these indices of $\hat Q_n$ and their asymptotic dispersions are carried out for distributions on the sphere $S^d$ (directional spaces), real projective space $\mathbb{R}P^{N-1}$ (axial spaces) and $\mathbb{C} P^{k-2}$ (planar shape spaces).

Overview

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1214/aos/1046294456

Cites

44 of 44 references verified0 citation errors · 0 not checkable

Statistics

Verification

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Citations

Cites

Show all 44 references

Cited by

See all 401

Metadata

Authors
Bhattacharya, R., & Patrangenaru, V.
Venue
The Annals of Statistics
Publisher
Institute of Mathematical Statistics
Published
2003-02-01
Volume
31
Issue
1
Pages
1-29
ISSN
0090-5364 (ISSN-L)
DOI
10.1214/aos/1046294456
OpenAlex
W2072931016
Cited by
401
References
44
FWCI
11.73
Type
journal article
Language
en
Open access
bronze

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review

How to cite

Cite CoChat for the checks on this page, and the paper for its own findings.

This page
CoChat. (2026). Citation check: Large sample theory of intrinsic and extrinsic sample means on manifolds. https://app.cochat.ai/papers/10.1214/aos/1046294456
The paper
Bhattacharya, R., & Patrangenaru, V. (2003). Large sample theory of intrinsic and extrinsic sample means on manifolds. The Annals of Statistics. https://doi.org/10.1214/aos/1046294456

Data sources

Bibliographic data: Semantic Scholar, OpenAlex, Crossref.

Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).

Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.