Nonparametric analysis of non-euclidean data on shapes and images

Rabi Bhattacharya, Rachel Oliver

Research output: Contribution to journalArticlepeer-review


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)
Pages (from-to)1-36
Number of pages36
JournalSankhya: The Indian Journal of Statistics
StatePublished - 2019


  • Density estimation
  • Fréchet means
  • 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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