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Journal Articles Bernoulli Year : 2020

Kernel and wavelet density estimators on manifolds and more general metric spaces

Galatia Cleanthous
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Athanasios G Georgiadis
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Pencho Petrushev
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Dominique Picard

Abstract

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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hal-03916487 , version 1 (30-12-2022)

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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, 2020, 26, ⟨10.3150/19-bej1171⟩. ⟨hal-03916487⟩
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