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Model selection for (auto-)regression with dependent data
Published online by Cambridge University Press: 15 August 2002
Abstract
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'
Cp. We state non asymptotic risk bounds for our estimator in
some ${\mathbb{L}}_2$-norm and we show that it is adaptive in the minimax
sense over a large class of Besov balls of the form Bα,p,∞(R) with p ≥ 1.
Keywords
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- Research Article
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- © EDP Sciences, SMAI, 2001