Adaptive estimation in autoregression or β-mixing regression via model selection

• 成果类型: Article
• 署名作者: Baraud, Y; Comte, F; Viennet, G
• 署名单位: Universite PSL; Ecole Normale Superieure (ENS); Universite Paris Cite; Sorbonne Universite; Universite Paris Cite; Sorbonne Universite
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 2001
• 页码: 839-875
• 关键词: Empirical Processes; DENSITY-ESTIMATION; bounds; inequalities; INFORMATION; prediction; ORDER; cp

摘要

We study the problem of estimating some 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.