JRSSB Aug 11, 2026

Quantiles on global non-positive curvature spaces

Authors
Hee-Seok Oh Ha-Young Shin
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Paper Information
  • Journal:
    Journal of the Royal Statistical Society Series B
  • DOI:
    10.1093/jrsssb/qkag121
  • Published:
    August 11, 2026
  • Added to Tracker:
    Aug 12, 2026
Abstract

Abstract We propose a notion of geometric quantiles on Hadamard spaces, or global non-positive curvature spaces. After providing some definitions and basic properties, including scaled isometry equivariance and a necessary condition on the gradient of the quantile loss function, we investigate asymptotic properties, such as strong consistency and joint asymptotic normality. We provide a detailed description of how to compute quantiles using a gradient descent algorithm in hyperbolic space. We detail several potential uses for these quantiles—defining measures of distributional characteristics, detecting outliers via a transformation–retransformation procedure, and testing the equality of distributions—and demonstrate their application through simulations and real biological data.

Author Details
Hee-Seok Oh
Author
Ha-Young Shin
Author
Citation Information
APA Format
Hee-Seok Oh & Ha-Young Shin (2026) . Quantiles on global non-positive curvature spaces. Journal of the Royal Statistical Society Series B , 10.1093/jrsssb/qkag121.
BibTeX Format
@article{paper1507,
  title = { Quantiles on global non-positive curvature spaces },
  author = { Hee-Seok Oh and Ha-Young Shin },
  journal = { Journal of the Royal Statistical Society Series B },
  year = { 2026 },
  doi = { 10.1093/jrsssb/qkag121 },
  url = { https://doi.org/10.1093/jrsssb/qkag121 }
}
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