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June, 1990 Nonparametric Estimation of a Probability Density on a Riemannian Manifold Using Fourier Expansions
Harrie Hendriks
Ann. Statist. 18(2): 832-849 (June, 1990). DOI: 10.1214/aos/1176347628

Abstract

Supposing a given collection $y_1, \cdots, y_N$ of i.i.d. random points on a Riemannian manifold, we discuss how to estimate the underlying distribution from a differential geometric viewpoint. The main hypothesis is that the manifold is closed and that the distribution is (sufficiently) smooth. Under such a hypothesis a convergence arbitrarily close to the $N^{-1/2}$ rate is possible, both in the $L_2$ and the $L_\infty$ senses.

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Harrie Hendriks. "Nonparametric Estimation of a Probability Density on a Riemannian Manifold Using Fourier Expansions." Ann. Statist. 18 (2) 832 - 849, June, 1990. https://doi.org/10.1214/aos/1176347628

Information

Published: June, 1990
First available in Project Euclid: 12 April 2007

zbMATH: 0711.62036
MathSciNet: MR1056339
Digital Object Identifier: 10.1214/aos/1176347628

Subjects:
Primary: 62G05
Secondary: 35P20, 58G11, 58G25

Rights: Copyright © 1990 Institute of Mathematical Statistics

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Vol.18 • No. 2 • June, 1990
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