Nonparametric Analysis of Non-Euclidean Data on Shapes and Images

Rabi Bhattacharya, Rachel Oliver

Research output: Contribution to journalReview articlepeer-review

3 Scopus citations


The article presents some of the basic theory for nonparametric inference on non-Euclidean spaces using Fréchet means that has been developed during the past two decades. Included are recent results on the asymptotic distribution theory of sample Fréchet means on such spaces, especially differentiable and Riemannian manifolds. Apart from this main theme and its applications, a nonparametric Bayes theory on Riemannian manifolds is outlined for the purpose of density estimation and classification. A final section briefly discusses the problem of machine vision, or robotic recognition of images as Riemannian manifolds.

Original languageEnglish (US)
JournalSankhya A
Issue number1
StatePublished - Feb 1 2019


  • Fréchet means
  • Primary 60F05, 62E20 60E05
  • Secondary 62G20
  • density estimation
  • machine vision
  • nonparametric Bayes on manifolds
  • uniqueness and asymptotic distribution

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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