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arXiv · 1304.7668

Adaptive estimation under single-index constraint in a regression model

Oleg Lepski·Nora Serdyukova
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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 Hölder and Nikol'skii functional classes, respectively.

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Oleg Lepski, Nora Serdyukova. 2014-01-28. Adaptive estimation under single-index constraint in a regression model. https://doi.org/10.1214/13-aos1152

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