We study the problem of estimatingsome unknown regression function
in a $\beta$-mixing dependent framework. To this end, we consider some
collection of models which are finite dimensional spaces. A penalized
least-squares estimator (PLSE) is built on a data driven selected model among
this collection. We state non asymptotic risk bounds for this PLSE and give
several examples where the procedure can be applied (autoregression, regression
with arithmetically $\beta$-mixing design points, regression with mixing
errors, estimation in additive frameworks, estimation of the order of the
autoregression). In addition we show that under a weak moment condition on the
errors, our estimator is adaptive in the minimax sense simultaneously over some
family of Besov balls.
Publié le : 2001-06-14
Classification:
Nonparametric regression,
least-squares estimator,
model selection,
adaptive estimation,
autoregression order,
additive framework,
time series,
mixing processes,
62G08,
62J02.
@article{1009210692,
author = {Baraud, Y and Comte, F. and Viennet, G.},
title = {Adaptive estimation in autoregression or -mixing regression via
model selection},
journal = {Ann. Statist.},
volume = {29},
number = {2},
year = {2001},
pages = { 839-875},
language = {en},
url = {http://dml.mathdoc.fr/item/1009210692}
}
Baraud, Y; Comte, F.; Viennet, G. Adaptive estimation in autoregression or -mixing regression via
model selection. Ann. Statist., Tome 29 (2001) no. 2, pp. 839-875. http://gdmltest.u-ga.fr/item/1009210692/