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December 2001 Sharp Adaptive Estimation of Linear Functionals
Jussi Klemelä, Alexandre B. Tsybakov
Ann. Statist. 29(6): 1567-1600 (December 2001). DOI: 10.1214/aos/1015345955


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.


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Jussi Klemelä. Alexandre B. Tsybakov. "Sharp Adaptive Estimation of Linear Functionals." Ann. Statist. 29 (6) 1567 - 1600, December 2001.


Published: December 2001
First available in Project Euclid: 5 March 2002

zbMATH: 1043.62029
MathSciNet: MR1891739
Digital Object Identifier: 10.1214/aos/1015345955

Primary: 62G05 , 62G20

Keywords: Adaptive curve estimation , Bandwidth selection , exact constants in nonparametric smoothing , Gaussian white noise , Kernel estimation , minimax risk

Rights: Copyright © 2001 Institute of Mathematical Statistics


Vol.29 • No. 6 • December 2001
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