Geodesic
Model selection for (auto-)regression with dependent data
ESAIM: Probability and Statistics, Tome 5 (2001), pp. 33-49

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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},
     publisher = {EDP-Sciences},
     volume = {5},
     year = {2001},
     mrnumber = {1845321},
     zbl = {0990.62035},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PS_2001__5__33_0/}
}
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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/