Geodesic
Model selection for (auto-)regression with dependent data
ESAIM: Probability and Statistics, Tome 5 (2001), pp. 33-49 Cet article a éte moissonné depuis la source Numdam

Voir la notice de l'article

In this paper, we study the problem of non parametric estimation of an unknown regression function from dependent data with sub-gaussian errors. As a particular case, we handle the autoregressive framework. For this purpose, we consider a collection of finite dimensional linear spaces (e.g. linear spaces spanned by wavelets or piecewise polynomials on a possibly irregular grid) and we estimate the regression function by a least-squares estimator built on a data driven selected linear space among the collection. This data driven choice is performed via the minimization of a penalized criterion akin to the Mallows’ C p . We state non asymptotic risk bounds for our estimator in some Ł 2 -norm and we show that it is adaptive in the minimax sense over a large class of Besov balls of the form ℬ α,p,∞ (R) with p≥1.

Classification : 62G08, 62J02
Keywords: nonparametric regression, least-squares estimator, adaptive estimation, autoregression, mixing processes 
@article{PS_2001__5__33_0,
     author = {Baraud, Yannick and Comte, F. and Viennet, G.},
     title = {Model selection for (auto-)regression with dependent data},
     journal = {ESAIM: Probability and Statistics},
     pages = {33--49},
     year = {2001},
     publisher = {EDP-Sciences},
     volume = {5},
     mrnumber = {1845321},
     zbl = {0990.62035},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PS_2001__5__33_0/}
}
TY  - JOUR
AU  - Baraud, Yannick
AU  - Comte, F.
AU  - Viennet, G.
TI  - Model selection for (auto-)regression with dependent data
JO  - ESAIM: Probability and Statistics
PY  - 2001
SP  - 33
EP  - 49
VL  - 5
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/item/PS_2001__5__33_0/
LA  - en
ID  - PS_2001__5__33_0
ER  - 
%0 Journal Article
%A Baraud, Yannick
%A Comte, F.
%A Viennet, G.
%T Model selection for (auto-)regression with dependent data
%J ESAIM: Probability and Statistics
%D 2001
%P 33-49
%V 5
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/item/PS_2001__5__33_0/
%G en
%F PS_2001__5__33_0
Baraud, Yannick; Comte, F.; Viennet, G. Model selection for (auto-)regression with dependent data. ESAIM: Probability and Statistics, Tome 5 (2001), pp. 33-49. http://geodesic.mathdoc.fr/item/PS_2001__5__33_0/