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Februrary 2003 Wavelet threshold estimation for additive regression models
Shuanglin Zhang, Man-Yu Wong
Ann. Statist. 31(1): 152-173 (Februrary 2003). DOI: 10.1214/aos/1046294460


Additive regression models have turned out to be useful statistical tools in the analysis of high-dimensional data. The attraction of such models is that the additive component can be estimated with the same optimal convergence rate as a one-dimensional nonparametric regression. However, this optimal property holds only when all the additive components have the same degree of "homogeneous" smoothness. In this paper, we propose a two-step wavelet thresholding estimation process in which the estimator is adaptive to different degrees of smoothness in different components and also adaptive to the "inhomogeneous" smoothness described by the Besov space. The estimator of an additive component constructed by the proposed procedure is shown to attain theone-dimensional optimal convergence rate even when the components have different degrees of "inhomogeneous" smoothness.


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Shuanglin Zhang. Man-Yu Wong. "Wavelet threshold estimation for additive regression models." Ann. Statist. 31 (1) 152 - 173, Februrary 2003.


Published: Februrary 2003
First available in Project Euclid: 26 February 2003

zbMATH: 1018.62031
MathSciNet: MR1962502
Digital Object Identifier: 10.1214/aos/1046294460

Primary: 62G07
Secondary: 62G20

Keywords: additive regression , Besov space , Local polynomial estimation , optimal convergence rate , threshold , Wavelet estimation

Rights: Copyright © 2003 Institute of Mathematical Statistics


Vol.31 • No. 1 • Februrary 2003
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