Journal
ESAIM-PROBABILITY AND STATISTICS
Volume 17, Issue -, Pages 635-649Publisher
EDP SCIENCES S A
DOI: 10.1051/ps/2012015
Keywords
Circular data; Frechet mean; uniqueness
Categories
Funding
- French Agence Nationale de la Recherche (ANR) [ANR-JCJC-SIMI1 DEMOS]
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Let (S-1, d(S1)) be the unit circle in R-2 endowed with the arclength distance. We give a sufficient and necessary condition for a general probability measure mu to admit a well defined Frechet mean on (S-1, d(S1)). We derive a new sufficient condition of existence P(alpha,phi) with no restriction on the support of the measure. Then, we study the convergence of the empirical Frechet mean to the Frechet mean and we give an algorithm to compute it.
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