In this paper we study the aggregation problem that can be formulated as follows. Assume that we have a family of estimators $\mathcal{F}$ built on the basis of available observations. The goal is to construct a new estimator whose risk is as close as possible to that of the best estimator in the family. We propose a general aggregation scheme that is universal in the following sense: it applies for families of arbitrary estimators and a wide variety of models and global risk measures. The procedure is based on comparison of empirical estimates of certain linear functionals with estimates induced by the family $\mathcal{F}$ . We derive oracle inequalities and show that they are unimprovable in some sense. Numerical results demonstrate good practical behavior of the procedure.
Publié le : 2009-02-15
Classification:
Aggregation,
lower bound,
normal means model,
oracle inequalities,
sparse vectors,
white noise model,
62G08,
62G05,
62G20
@article{1232115945,
author = {Goldenshluger, Alexander},
title = {A universal procedure for aggregating estimators},
journal = {Ann. Statist.},
volume = {37},
number = {1},
year = {2009},
pages = { 542-568},
language = {en},
url = {http://dml.mathdoc.fr/item/1232115945}
}
Goldenshluger, Alexander. A universal procedure for aggregating estimators. Ann. Statist., Tome 37 (2009) no. 1, pp. 542-568. http://gdmltest.u-ga.fr/item/1232115945/