|ADAPTIVE ESTIMATION UNDER SINGLE-INDEX CONSTRAINT IN A REGRESSION MODEL |
Auteur(s): Lepski O., Serdyukova Nora
(Article) Publié: Annals Of Statistics, vol. 42 p.1-28. (2014)
Ref HAL: hal-01265248_v1
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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.