Intrinsic Hölder classes of density functions on Riemannian manifolds and lower bounds to convergence rates

Dohyeong Ki and Byeong U. Park

Statistics & Probability Letters, 2021, vol. 169, issue C

Abstract: We consider Hölder classes of density functions on Riemannian manifolds in intrinsic perspectives. We develop a theorem that links such Hölder classes on Riemannian manifolds to those on Euclidean spaces. Using the theorem, we derive lower bounds to Lp-convergence rates (1≤p≤∞) for the estimation of the underlying density on a Riemannian manifold.

Keywords: Nonparametric density estimation; Convergence rates; Riemannian manifolds; Lp-convergence (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1016/j.spl.2020.108959

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