A data-driven estimate is given that, over a Sobolev space, is simultaneously asymptotically sharp minimax for estimating both the function and its derivatives under integrated squared error loss. It is also shown that linear estimates cannot be simultaneously asymptotically sharp minimax over a given Sobolev space.
Publié le : 1998-02-14
Classification:
Adaptation,
Sobolev functions,
minimax,
linear estimates,
filtering,
62C05,
62E20,
62J02,
62G05,
62M99
@article{1030563985,
author = {Efromovich, Sam},
title = {Simultaneous sharp estimation of functions and their derivatives},
journal = {Ann. Statist.},
volume = {26},
number = {3},
year = {1998},
pages = { 273-278},
language = {en},
url = {http://dml.mathdoc.fr/item/1030563985}
}
Efromovich, Sam. Simultaneous sharp estimation of functions and their derivatives. Ann. Statist., Tome 26 (1998) no. 3, pp. 273-278. http://gdmltest.u-ga.fr/item/1030563985/