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Nonparametric Analysis of Non-Euclidean Data on Shapes and Images

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Abstract

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.

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Funding

Rachel Oliver was partially funded by NSF CCF 1740858, TRIPODS. Rabi Bhattacharya was partially supported by the NSF grant DMS 1406872.

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  1. Department of Mathematics, University of Arizona, 617 N. Santa Rita Avenue, P.O. Box 210089, Tucson, AZ, 85721-0089, USA

    Rabi Bhattacharya & Rachel Oliver

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  1. Rabi Bhattacharya
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Bhattacharya, R., Oliver, R. Nonparametric Analysis of Non-Euclidean Data on Shapes and Images. Sankhya A 81, 1–36 (2019). https://doi.org/10.1007/s13171-018-0127-9

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