The minimax theory for estimating linear functionals is extended to the case of a finite union of convex parameter spaces. Upper and lower bounds for the minimax risk can still be described in terms of a modulus of continuity. However in contrast to the theory for convex parameter spaces rate optimal procedures are often required to be nonlinear. A construction of such nonlinear procedures is given. The results developed in this paper have important applications to the theory of adaptation.
Publié le : 2004-04-14
Classification:
Constrained risk inequality,
linear functionals,
minimax estimation,
modulus of continuity,
nonparametric functional estimation,
white noise model,
62G99,
62F12,
62C20,
62M99
@article{1083178938,
author = {Cai, T. Tony and Low, Mark G.},
title = {Minimax estimation of linear functionals over nonconvex parameter spaces},
journal = {Ann. Statist.},
volume = {32},
number = {1},
year = {2004},
pages = { 552-576},
language = {en},
url = {http://dml.mathdoc.fr/item/1083178938}
}
Cai, T. Tony; Low, Mark G. Minimax estimation of linear functionals over nonconvex parameter spaces. Ann. Statist., Tome 32 (2004) no. 1, pp. 552-576. http://gdmltest.u-ga.fr/item/1083178938/