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February 2014 Adaptive estimation under single-index constraint in a regression model
Oleg Lepski, Nora Serdyukova
Ann. Statist. 42(1): 1-28 (February 2014). DOI: 10.1214/13-AOS1152

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. "Adaptive estimation under single-index constraint in a regression model." Ann. Statist. 42 (1) 1 - 28, February 2014. https://doi.org/10.1214/13-AOS1152

Information

Published: February 2014
First available in Project Euclid: 15 January 2014

zbMATH: 1302.62077
MathSciNet: MR3161459
Digital Object Identifier: 10.1214/13-AOS1152

Subjects:
Primary: 62G05
Secondary: 62G08 , 62G20

Keywords: adaptive estimation , lower bounds , Minimax rate , Nonparametric regression , Oracle inequalities , Single-index model , structural adaptation

Rights: Copyright © 2014 Institute of Mathematical Statistics

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Vol.42 • No. 1 • February 2014
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