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We consider the problem of estimating the density of observations takingvalues in classical or nonclassical spaces such as manifolds and more generalmetric spaces. Our setting is quite general but also sufficiently rich inallowing the development of smooth functional calculus with well localizedspectral kernels, Besov regularity spaces, and wavelet type systems. Kernel andboth linear and nonlinear wavelet density estimators are introduced andstudied. Convergence rates for these estimators are established, which areanalogous to the existing results in the classical setting of real-valuedvariables.

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