Model selection for (auto-)regression with dependent data

Baraud, Yannick; Comte, F.; Viennet, G.

Baraud, Yannick ; Comte, F. ; Viennet, G.

ESAIM: Probability and Statistics, Tome 5 (2001), pp. 33-49.

Résumé

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 $ℬ_{α, p, \infty} (R)$ with $p \geq 1$ .

MR Zbl | 5 citations dans Numdam

Classification : 62G08, 62J02
Mots clés : nonparametric regression, least-squares estimator, adaptive estimation, autoregression, mixing processes

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     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://www.numdam.org/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://www.numdam.org/item/PS_2001__5__33_0/

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