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

G. Cleanthous, Athanasios Georgiadis, G. Kerkyacharian, P. Petrushev, D. Picard

Research output: Working paperResearch

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, which are analogous to the existing results in the classical setting of real-valued variables.
Original languageEnglish
PublisherArXiv
Number of pages35
Publication statusPublished - 2018

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Wavelet Estimator
Density Estimator
Metric space
kernel
Functional Calculus
Type Systems
Convergence Rate
Wavelets
Regularity
Estimator
Observation

Cite this

Cleanthous, G., Georgiadis, A., Kerkyacharian, G., Petrushev, P., & Picard, D. (2018). Kernel and wavelet density estimators on manifolds and more general metric spaces. ArXiv.
Cleanthous, G. ; Georgiadis, Athanasios ; Kerkyacharian, G. ; Petrushev, P. ; Picard, D. / Kernel and wavelet density estimators on manifolds and more general metric spaces. ArXiv, 2018.
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Cleanthous, G, Georgiadis, A, Kerkyacharian, G, Petrushev, P & Picard, D 2018 'Kernel and wavelet density estimators on manifolds and more general metric spaces' ArXiv.

Kernel and wavelet density estimators on manifolds and more general metric spaces. / Cleanthous, G.; Georgiadis, Athanasios; Kerkyacharian, G. ; Petrushev, P.; Picard, D.

ArXiv, 2018.

Research output: Working paperResearch

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AU - Cleanthous, G.

AU - Georgiadis, Athanasios

AU - Kerkyacharian, G.

AU - Petrushev, P.

AU - Picard, D.

PY - 2018

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N2 - 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, which are analogous to the existing results in the classical setting of real-valued variables.

AB - 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, which are analogous to the existing results in the classical setting of real-valued variables.

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Cleanthous G, Georgiadis A, Kerkyacharian G, Petrushev P, Picard D. Kernel and wavelet density estimators on manifolds and more general metric spaces. ArXiv. 2018.