We propose a procedure to handle the problem of Gaussian regression when the variance is unknown. We mix least-squares estimators from various models according to a procedure inspired by that of Leung and Barron [IEEE Trans. Inform. Theory 52 (2006) 3396–3410]. We show that in some cases, the resulting estimator is a simple shrinkage estimator. We then apply this procedure to perform adaptive estimation in Besov spaces. Our results provide non-asymptotic risk bounds for the Euclidean risk of the estimator.
Publié le : 2008-11-15
Classification:
adaptive minimax estimation,
Gibbs mixture,
linear regression,
oracle inequalities,
shrinkage estimator
@article{1225980572,
author = {Giraud, Christophe},
title = {Mixing least-squares estimators when the variance is unknown},
journal = {Bernoulli},
volume = {14},
number = {1},
year = {2008},
pages = { 1089-1107},
language = {en},
url = {http://dml.mathdoc.fr/item/1225980572}
}
Giraud, Christophe. Mixing least-squares estimators when the variance is unknown. Bernoulli, Tome 14 (2008) no. 1, pp. 1089-1107. http://gdmltest.u-ga.fr/item/1225980572/