Volume 17, 2013
|Page(s)||635 - 649|
|Published online||04 November 2013|
Necessary and sufficient condition for the existence of a Fréchet mean on the circle
Institut de Mathématiques de Toulouse Université de Toulouse et CNRS (UMR 5219), F-31062 Toulouse, France
Received: 1 August 2011
Revised: 9 February 2012
Let () be the unit circle in ℝ2 endowed with the arclength distance. We give a sufficient and necessary condition for a general probability measure μ to admit a well defined Fréchet mean on (). We derive a new sufficient condition of existence P(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.
Mathematics Subject Classification: 62H11
Key words: Circular data / Fréchet mean / uniqueness
© EDP Sciences, SMAI, 2013
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