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Klemelä, Jussi; Tsybakov, Alexandre B.

Sharp adaptive estimation of linear functionals. (English) Zbl 1043.62029

Ann. Stat. 29, No. 6, 1567-1600 (2001).
Summary: We consider estimation of a linear functional \(T(f)\) where \(f\) is an unknown function observed in Gaussian white noise. We find asymptotically sharp adaptive estimators on various scales of smoothness classes in multidimensional situations. The results allow evaluating explicitly the effect of dimension and treating general scales of classes. Furthermore, we establish a connection between sharp adaptation and optimal recovery. Namely, we propose a scheme that reduces the construction of sharp adaptive estimators on a scale of functional classes to a solution of the corresponding optimization problem.

Cited in 16 Documents

MSC:

62G07 Density estimation
62G05 Nonparametric estimation
62G20 Asymptotic properties of nonparametric inference

Keywords:

adaptive curve estimation; bandwidth selection; kernel estimation; minimax risk; exact constants in nonparametric smoothing
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