arbiter
JournalsAccount

Generalized Fréchet means with random minimizing domains and its strong consistency

Jaesung Park & Sungkyu Jung

Biometrika2026https://doi.org/10.1093/biomet/asag002article
AJG 4ABDC A*
Weight
0.37

Abstract

Summary This paper introduces a novel extension of Fréchet means, referred to as generalized Fréchet means, as a comprehensive framework for describing the characteristics of random elements. The generalized Fréchet mean is defined as the minimizer of a cost function, and the framework encompasses various extensions of Fréchet means that have appeared in the literature. The most distinctive feature of the proposed framework is that it allows the domain of minimization for the empirical generalized Fréchet means to be random and different from that of its population counterpart. This flexibility broadens the applicability of the Fréchet mean framework to various statistical scenarios, including sequential dimension reduction for non-Euclidean data. We establish a strong consistency theorem for generalized Fréchet means and demonstrate the utility of the proposed framework by verifying the consistency of principal geodesic analysis on the hypersphere.

1 citation

Open via your library →

Cite this paper

https://doi.org/https://doi.org/10.1093/biomet/asag002

Or copy a formatted citation

@article{jaesung2026,
  title        = {{Generalized Fréchet means with random minimizing domains and its strong consistency}},
  author       = {Jaesung Park & Sungkyu Jung},
  journal      = {Biometrika},
  year         = {2026},
  doi          = {https://doi.org/https://doi.org/10.1093/biomet/asag002},
}

Paste directly into BibTeX, Zotero, or your reference manager.

Flag this paper

Generalized Fréchet means with random minimizing domains and its strong consistency

Flags are reviewed by the Arbiter methodology team within 5 business days.

Evidence weight

0.37

Balanced mode · F 0.40 / M 0.15 / V 0.05 / R 0.40

F · citation impact0.16 × 0.4 = 0.06
M · momentum0.53 × 0.15 = 0.08
V · venue signal0.50 × 0.05 = 0.03
R · text relevance †0.50 × 0.4 = 0.20

† Text relevance is estimated at 0.50 on the detail page — for your query’s actual relevance score, open this paper from a search result.