圆上Fréchet平均存在的充要条件
Necessary and sufficient condition for the existence of a Fréchet mean on the circle
摘要：
设$(§^1,d_{§^1})$为$\R^2$中的单位圆，赋予弧长距离。本文给出了一般概率测度$μ$在$(§^1,d_{§^1})$上存在一个定义良好的Fréchet平均的充必要条件. %此准则允许恢复已知的存在的充分条件。我们得到了一个新的存在性充分条件$P(α,φ)$没有限制的支持度的措施。然后，我们研究了经验Fréchet平均到Fréchet平均的收敛性，并给出了计算它的一个算法.
英文摘要：
Let $(§^1,d_{§^1})$ be the unit circle in $\R^2$ 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 $(§^1,d_{§^1})$. %This criterion allows to recover already known sufficient conditions of existence. 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
