The problem of nonparametric function estimation in the Gaussian
white noise model is considered. It is assumed that the unknown function
belongs to one of the Sobolev classes, with an unknown regularity parameter.
Asymptotically exact adaptive estimators of functions are proposed on the scale
of Sobolev classes, with respect to pointwise and sup-norm risks. It is shown
that, unlike the case of $L_2$-risk, a loss of efficiency under adaptation is
inevitable here. Bounds on the value of the loss of efficiency are
obtained.
Publié le : 1998-12-14
Classification:
Gaussian white noise,
adaptive nonparametric estimation,
Sobolev class,
loss of efficiency under adaptation,
minimax risk,
exact constants,
62G05,
62G20
@article{1024691478,
author = {Tsybakov, A. B.},
title = {Pointwise and sup-norm sharp adaptive estimation of functions on
the Sobolev classes},
journal = {Ann. Statist.},
volume = {26},
number = {3},
year = {1998},
pages = { 2420-2469},
language = {en},
url = {http://dml.mathdoc.fr/item/1024691478}
}
Tsybakov, A. B. Pointwise and sup-norm sharp adaptive estimation of functions on
the Sobolev classes. Ann. Statist., Tome 26 (1998) no. 3, pp. 2420-2469. http://gdmltest.u-ga.fr/item/1024691478/