Adaptive estimation of linear functionals over a collection of parameter spaces is considered. A between-class modulus of continuity, a geometric quantity, is shown to be instrumental in characterizing the degree of adaptability over two parameter spaces in the same way that the usual modulus of continuity captures the minimax difficulty of estimation over a single parameter space. A general construction of optimally adaptive estimators based on an ordered modulus of continuity is given. The results are complemented by several illustrative examples.
Publié le : 2005-10-14
Classification:
Adaptive estimation,
between-class modulus of continuity,
cost of adaptation,
linear functional,
ordered modulus of continuity,
white noise model,
62G99,
62F12,
62F35,
62M99
@article{1132936565,
author = {Cai, T. Tony and Low, Mark G.},
title = {On adaptive estimation of linear functionals},
journal = {Ann. Statist.},
volume = {33},
number = {1},
year = {2005},
pages = { 2311-2343},
language = {en},
url = {http://dml.mathdoc.fr/item/1132936565}
}
Cai, T. Tony; Low, Mark G. On adaptive estimation of linear functionals. Ann. Statist., Tome 33 (2005) no. 1, pp. 2311-2343. http://gdmltest.u-ga.fr/item/1132936565/