Model selection for regression on a fixed design |
| |
Authors: | Yannick Baraud |
| |
Affiliation: | (1) DMA, Ecole Normale Supérieure, 45 rue d'Ulm, 75230 Paris Cedex 05, France. e-mail: yannick.baraud@ens.fr, FR |
| |
Abstract: | We deal with the problem of estimating some unknown regression function involved in a regression framework with deterministic design points. For this end, we consider some collection of finite dimensional linear spaces (models) and the least-squares estimator built on a data driven selected model among this collection. This data driven choice is performed via the minimization of some penalized model selection criterion that generalizes on Mallows' C p . We provide non asymptotic risk bounds for the so-defined estimator from which we deduce adaptivity properties. Our results hold under mild moment conditions on the errors. The statement and the use of a new moment inequality for empirical processes is at the heart of the techniques involved in our approach. Received: 2 July 1997 / Revised version: 20 September 1999 / Published online: 6 July 2000 |
| |
Keywords: | and phrases: Nonparametric regression – Least-squares estimator – Model selection – Adaptive estimation – Moment inequality – Concentration of measure – Empirical processes |
本文献已被 SpringerLink 等数据库收录! |