Some properties of Fréchet medians in Riemannian manifolds

2011/10/18 by Le Yang, Yang, Le
Computer Science · Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Morphological variations and asymmetry #Point processes and geometric inequalities #Probability (math.PR) #Statistics Theory (math.ST) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1110.3899

openalex publication_date 2011/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The consistency of Fréchet medians is proved for probability measures in proper metric spaces. In the context of Riemannian manifolds, assuming that the probability measure has more than a half mass lying in a convex ball and verifies some concentration conditions, the positions of its Fréchet medians are estimated. It is also shown that, in compact Riemannian manifolds, the Fréchet sample medians of generic data points are always unique.

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