Geometric structures arising from kernel density estimation on Riemannian manifolds

Authors:
Yoon Tae Kim;Hyun Suk Park
Affiliations:
-;-
Venue:
Journal of Multivariate Analysis
Year:
2013

Citing 3
Cited 0

Kernel estimators of density function of directional data

Journal of Multivariate Analysis - Memorial volume dedicated to P. R. Krishnaiah
Spherical deconvolution

Journal of Multivariate Analysis
Application of fast spherical Fourier transform to density estimation

Journal of Multivariate Analysis

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Abstract

Estimating the kernel density function of a random vector taking values on Riemannian manifolds is considered. We make use of the concept of exponential map in order to define the kernel density estimator. We study the asymptotic behavior of the kernel estimator which contains geometric quantities (i.e. the curvature tensor and its covariant derivatives). Under a Holder class of functions defined on a Riemannian manifold with some global losses, the L"2-minimax rate and its relative efficiency are obtained.