Selection of variables and dimension reduction in high-dimensional non-parametric regression
| dc.creator | Bertin, Karine | |
| dc.creator | Lecué, Guillaume | |
| dc.date | 2008-11-07 | |
| dc.date | 2008-12-16 | |
| dc.date.accessioned | 2026-07-07T12:12:38Z | |
| dc.date.available | 2026-07-07T12:12:38Z | |
| dc.description | We consider a $l_1$-penalization procedure in the non-parametric Gaussian regression model. In many concrete examples, the dimension $d$ of the input variable $X$ is very large (sometimes depending on the number of observations). Estimation of a $β$-regular regression function $f$ cannot be faster than the slow rate $n^{-2β/(2β+d)}$. Hopefully, in some situations, $f$ depends only on a few numbers of the coordinates of $X$. In this paper, we construct two procedures. The first one selects, with high probability, these coordinates. Then, using this subset selection method, we run a local polynomial estimator (on the set of interesting coordinates) to estimate the regression function at the rate $n^{-2β/(2β+d^*)}$, where $d^*$, the "real" dimension of the problem (exact number of variables whom $f$ depends on), has replaced the dimension $d$ of the design. To achieve this result, we used a $l_1$ penalization method in this non-parametric setup. | |
| dc.description | Published in at http://dx.doi.org/10.1214/08-EJS327 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/0811.1115 | |
| dc.identifier | http://arxiv.org/abs/0811.1115 | |
| dc.identifier | Electronic Journal of Statistics 2008, Vol. 2, 1224-1241 | |
| dc.identifier | doi:10.1214/08-EJS327 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/210606 | |
| dc.subject | Statistics Theory | |
| dc.subject | 62G08 (Primary) | |
| dc.title | Selection of variables and dimension reduction in high-dimensional non-parametric regression | |
| dc.type | text |