Nonparametric Estimation of the Regression Function in an Errors-in-Variables Model
| dc.creator | Comte, Fabienne | |
| dc.creator | Taupin, Marie-Luce | |
| dc.date | 2005-11-04 | |
| dc.date.accessioned | 2026-07-07T09:19:40Z | |
| dc.date.available | 2026-07-07T09:19:40Z | |
| dc.description | We consider the regression model with errors-in-variables where we observe $n$ i.i.d. copies of $(Y,Z)$ satisfying $Y=f(X)+ξ, Z=X+σε$, involving independent and unobserved random variables $X,ξ,ε$. The density $g$ of $X$ is unknown, whereas the density of $σε$ is completely known. Using the observations $(Y\_i, Z\_i)$, $i=1,...,n$, we propose an estimator of the regression function $f$, built as the ratio of two penalized minimum contrast estimators of $\ell=fg$ and $g$, without any prior knowledge on their smoothness. We prove that its $\mathbb{L}\_2$-risk on a compact set is bounded by the sum of the two $\mathbb{L}\_2(\mathbb{R})$-risks of the estimators of $\ell$ and $g$, and give the rate of convergence of such estimators for various smoothness classes for $\ell$ and $g$, when the errors $ε$ are either ordinary smooth or super smooth. The resulting rate is optimal in a minimax sense in all cases where lower bounds are available. | |
| dc.identifier | https://arxiv.org/abs/math/0511111 | |
| dc.identifier | http://arxiv.org/abs/math/0511111 | |
| dc.identifier | Statistica Sinica 17 (2007) 1065-1090 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/154473 | |
| dc.subject | Statistics Theory | |
| dc.subject | (Primary) 62G08, 62G07; (Secondary) 62G05, 62G20 | |
| dc.title | Nonparametric Estimation of the Regression Function in an Errors-in-Variables Model | |
| dc.type | text |