Kernel and wavelet density estimators on manifolds and more general metric spaces
Résumé
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.
Mots clés
adaptive density estimators Ahlfors regularity Besov space heat kernel non-parametric estimators sample kernel density estimators wavelet density estimators
adaptive density estimators
Ahlfors regularity
Besov space
heat kernel
non-parametric estimators
sample kernel density estimators
wavelet density estimators
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