A general constrained minimum risk inequality is derived. Given two densities $f_{\theta}$ and $f_0$ we find a lower bound for the risk at the point $\theta$ given an upper bound for the risk at the point 0. The inequality
sheds new light on superefficient estimators in the normal location problem and also on an adaptive estimation problem arising in nonparametric functional estimation.
Publié le : 1996-12-14
Classification:
Adaptive estimation,
superefficient estimators,
nonparametric functional estimation,
minimum risk inequalities,
white noise model,
density estimation,
nonparametric regression,
62G99,
62F12,
62F35,
62M99
@article{1032181166,
author = {Brown, Lawrence D. and Low, Mark G.},
title = {A constrained risk inequality with applications to nonparametric functional estimation},
journal = {Ann. Statist.},
volume = {24},
number = {6},
year = {1996},
pages = { 2524-2535},
language = {en},
url = {http://dml.mathdoc.fr/item/1032181166}
}
Brown, Lawrence D.; Low, Mark G. A constrained risk inequality with applications to nonparametric functional estimation. Ann. Statist., Tome 24 (1996) no. 6, pp. 2524-2535. http://gdmltest.u-ga.fr/item/1032181166/