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.
Publié le : 2001-12-14
Classification:
Adaptive curve estimation,
bandwidth selection,
exact constants in nonparametric smoothing,
Gaussian white noise,
kernel estimation,
minimax risk,
62G05,
62G20
@article{1015345955,
author = {Klemel\"a, Jussi and Tsybakov, Alexandre B.},
title = {Sharp Adaptive Estimation of Linear Functionals},
journal = {Ann. Statist.},
volume = {29},
number = {2},
year = {2001},
pages = { 1567-1600},
language = {en},
url = {http://dml.mathdoc.fr/item/1015345955}
}
Klemelä, Jussi; Tsybakov, Alexandre B. Sharp Adaptive Estimation of Linear Functionals. Ann. Statist., Tome 29 (2001) no. 2, pp. 1567-1600. http://gdmltest.u-ga.fr/item/1015345955/