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Mathematics > Statistics Theory

arXiv:1304.7668 (math)
[Submitted on 29 Apr 2013 (v1), last revised 28 Jan 2014 (this version, v2)]

Title:Adaptive estimation under single-index constraint in a regression model

Authors: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.
Comments: Published in at this http URL the Annals of Statistics (this http URL) by the Institute of Mathematical Statistics (this http URL)
Subjects: Statistics Theory (math.ST); Probability (math.PR)
Report number: IMS-AOS-AOS1152
Cite as: arXiv:1304.7668 [math.ST]
  (or arXiv:1304.7668v2 [math.ST] for this version)
  https://doi.org/10.48550/arXiv.1304.7668
Journal reference: Annals of Statistics 2014, Vol. 42, No. 1, 1-28
Related DOI: https://doi.org/10.1214/13-AOS1152

Submission history

From: Oleg Lepski [view email] [via VTEX proxy]
[v1] Mon, 29 Apr 2013 14:22:21 UTC (69 KB)
[v2] Tue, 28 Jan 2014 09:30:38 UTC (55 KB)
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