Title: Nonparametric Analysis of Non-Euclidean Data on Shapes and Images

Author(s): Rabi Bhattacharya and Rachel Oliver
Issue: Volume 81 Series A Part 1 Year 2019
Pages: 1 -- 36
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.
Primary 60F05, 62E20 60E05; Secondary 62G20
Keywords and phrases: Fréchet means, uniqueness and asymptotic distribution, nonparametric Bayes on manifolds, density estimation, machine vision