# Necessary and sufficient condition for the existence of a Fréchet mean on the circle

ESAIM: Probability and Statistics (2013)

- Volume: 17, page 635-649
- ISSN: 1292-8100

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topCharlier, Benjamin. "Necessary and sufficient condition for the existence of a Fréchet mean on the circle." ESAIM: Probability and Statistics 17 (2013): 635-649. <http://eudml.org/doc/274376>.

@article{Charlier2013,

abstract = {Let ( $\mathbb \{S\}^1, d_\{\mathbb \{S\}^1\}$ S 1 , d S 1 ) be the unit circle in ℝ2 endowed with the arclength distance. We give a sufficient and necessary condition for a general probability measure μto admit a well defined Fréchet mean on ( $\mathbb \{S\}^1,d_\{\mathbb \{S\}^1\}$ S 1 , d S 1 ). We derive a new sufficient condition of existenceP(α, ϕ) with no restriction on the support of the measure. Then, we study the convergence of the empirical Fréchet mean to the Fréchet mean and we give an algorithm to compute it.},

author = {Charlier, Benjamin},

journal = {ESAIM: Probability and Statistics},

keywords = {circular data; fréchet mean; uniqueness; Fréchet mean},

language = {eng},

pages = {635-649},

publisher = {EDP-Sciences},

title = {Necessary and sufficient condition for the existence of a Fréchet mean on the circle},

url = {http://eudml.org/doc/274376},

volume = {17},

year = {2013},

}

TY - JOUR

AU - Charlier, Benjamin

TI - Necessary and sufficient condition for the existence of a Fréchet mean on the circle

JO - ESAIM: Probability and Statistics

PY - 2013

PB - EDP-Sciences

VL - 17

SP - 635

EP - 649

AB - Let ( $\mathbb {S}^1, d_{\mathbb {S}^1}$ S 1 , d S 1 ) be the unit circle in ℝ2 endowed with the arclength distance. We give a sufficient and necessary condition for a general probability measure μto admit a well defined Fréchet mean on ( $\mathbb {S}^1,d_{\mathbb {S}^1}$ S 1 , d S 1 ). We derive a new sufficient condition of existenceP(α, ϕ) with no restriction on the support of the measure. Then, we study the convergence of the empirical Fréchet mean to the Fréchet mean and we give an algorithm to compute it.

LA - eng

KW - circular data; fréchet mean; uniqueness; Fréchet mean

UR - http://eudml.org/doc/274376

ER -

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