Open Access
August 2020 Kernel and wavelet density estimators on manifolds and more general metric spaces
Galatia Cleanthous, Athanasios G. Georgiadis, Gerard Kerkyacharian, Pencho Petrushev, Dominique Picard
Bernoulli 26(3): 1832-1862 (August 2020). DOI: 10.3150/19-BEJ1171


We consider the problem of estimating the density of observations taking values in classical or nonclassical spaces such as manifolds and more general metric spaces. Our setting is quite general but also sufficiently rich in allowing the development of smooth functional calculus with well localized spectral kernels, Besov regularity spaces, and wavelet type systems. Kernel and both linear and nonlinear wavelet density estimators are introduced and studied. Convergence rates for these estimators are established and discussed.


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Galatia Cleanthous. Athanasios G. Georgiadis. Gerard Kerkyacharian. Pencho Petrushev. Dominique Picard. "Kernel and wavelet density estimators on manifolds and more general metric spaces." Bernoulli 26 (3) 1832 - 1862, August 2020.


Received: 1 March 2019; Revised: 1 August 2019; Published: August 2020
First available in Project Euclid: 27 April 2020

zbMATH: 07193944
MathSciNet: MR4091093
Digital Object Identifier: 10.3150/19-BEJ1171

Keywords: adaptive density estimators , Ahlfors regularity , Besov space , heat kernel , non-parametric estimators , sample kernel density estimators , wavelet density estimators

Rights: Copyright © 2020 Bernoulli Society for Mathematical Statistics and Probability

Vol.26 • No. 3 • August 2020
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