Geometric structures arising from kernel density estimation on Riemannian manifolds

DOI10.1016/j.jmva.2012.07.006zbMath1255.62104OpenAlexW1968165373WikidataQ115345767 ScholiaQ115345767MaRDI QIDQ1931857

Yoon Tae Kim, Hyun Suk Park

Publication date: 16 January 2013

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmva.2012.07.006

zbMATH Keywords

Riemannian manifoldsexponential mapkernel density estimatorrelative efficiencyminimax convergence rate

Mathematics Subject Classification ID

Density estimation (62G07) Estimation in multivariate analysis (62H12) Asymptotic properties of nonparametric inference (62G20) Local Riemannian geometry (53B20)

Related Items (9)

Intrinsic Hölder classes of density functions on Riemannian manifolds and lower bounds to convergence rates ⋮ A roughness penalty approach to estimate densities over two-dimensional manifolds ⋮ Density estimation on manifolds with boundary ⋮ Kernel density estimation on symmetric spaces of non-compact type ⋮ Diffusion maps for embedded manifolds with boundary with applications to PDEs ⋮ A Functional Data Analysis Approach to the Estimation of Densities over Complex Regions ⋮ Comparison of relative efficiency of kernel density estimator with the exponential map ⋮ Nonparametric recursive regression estimation on Riemannian manifolds ⋮ Graph-theoretic algorithms for Kolmogorov operators: approximating solutions and their gradients in elliptic and parabolic problems on manifolds

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