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

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 α,p, (R) with p1.

Classification: 62G08,  62J02
Keywords: nonparametric regression, least-squares estimator, adaptive estimation, autoregression, mixing processes
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     title = {Model selection for (auto-)regression with dependent data},
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Baraud, Yannick; Comte, F.; Viennet, G. Model selection for (auto-)regression with dependent data. ESAIM: Probability and Statistics, Volume 5 (2001), pp. 33-49. http://www.numdam.org/item/PS_2001__5__33_0/

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