Adaptive estimation under single-index constraint in a regression model
Abstract
The problem of adaptive multivariate function estimation in the single-index regression model with random design and weak assumptions on the noise is investigated. A novel estimation procedure that adapts simultaneously to the unknown index vector and the smoothness of the link function by selecting from a family of specific kernel estimators is proposed. We establish a pointwise oracle inequality which, in its turn, is used to judge the quality of estimating the entire function (``global'' oracle inequality). Both the results are applied to the problems of pointwise and global adaptive estimation over a collection of H\"{o}lder and Nikol'skii functional classes, respectively.
Cite
@article{arxiv.1304.7668,
title = {Adaptive estimation under single-index constraint in a regression model},
author = {Oleg Lepski and Nora Serdyukova},
journal= {arXiv preprint arXiv:1304.7668},
year = {2014}
}
Comments
Published in at http://dx.doi.org/10.1214/13-AOS1152 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)