Open Access
June 2001 Adaptive estimation in autoregression or -mixing regression via model selection
Y Baraud, F. Comte, G. Viennet
Ann. Statist. 29(3): 839-875 (June 2001). DOI: 10.1214/aos/1009210692


We study the problem of estimatingsome unknown regression function in a $\beta$-mixing dependent framework. To this end, we consider some collection of models which are finite dimensional spaces. A penalized least-squares estimator (PLSE) is built on a data driven selected model among this collection. We state non asymptotic risk bounds for this PLSE and give several examples where the procedure can be applied (autoregression, regression with arithmetically $\beta$-mixing design points, regression with mixing errors, estimation in additive frameworks, estimation of the order of the autoregression). In addition we show that under a weak moment condition on the errors, our estimator is adaptive in the minimax sense simultaneously over some family of Besov balls.


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Y Baraud. F. Comte. G. Viennet. "Adaptive estimation in autoregression or -mixing regression via model selection." Ann. Statist. 29 (3) 839 - 875, June 2001.


Published: June 2001
First available in Project Euclid: 24 December 2001

zbMATH: 1012.62034
MathSciNet: MR1865343
Digital Object Identifier: 10.1214/aos/1009210692

Primary: 62G08
Secondary: 62J02.

Keywords: adaptive estimation , additive framework , autoregression order , least-squares estimator , mixing processes , Model selection , Nonparametric regression , time series

Rights: Copyright © 2001 Institute of Mathematical Statistics

Vol.29 • No. 3 • June 2001
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