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Kernel and wavelet density estimators on manifolds and more general metric spaces. (English) Zbl 1439.62097

Summary: 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.

MSC:

62G07 Density estimation
62R30 Statistics on manifolds
62R20 Statistics on metric spaces
35K08 Heat kernel
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
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