Open Access
June 2010 Estimation in additive models with highly or nonhighly correlated covariates
Jiancheng Jiang, Yingying Fan, Jianqing Fan
Ann. Statist. 38(3): 1403-1432 (June 2010). DOI: 10.1214/09-AOS753


Motivated by normalizing DNA microarray data and by predicting the interest rates, we explore nonparametric estimation of additive models with highly correlated covariates. We introduce two novel approaches for estimating the additive components, integration estimation and pooled backfitting estimation. The former is designed for highly correlated covariates, and the latter is useful for nonhighly correlated covariates. Asymptotic normalities of the proposed estimators are established. Simulations are conducted to demonstrate finite sample behaviors of the proposed estimators, and real data examples are given to illustrate the value of the methodology.


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Jiancheng Jiang. Yingying Fan. Jianqing Fan. "Estimation in additive models with highly or nonhighly correlated covariates." Ann. Statist. 38 (3) 1403 - 1432, June 2010.


Published: June 2010
First available in Project Euclid: 8 March 2010

zbMATH: 1189.62072
MathSciNet: MR2662347
Digital Object Identifier: 10.1214/09-AOS753

Primary: 60J60 , 62G10
Secondary: 62G20

Keywords: Additive model , backfitting , local linear smoothing , normalization , varying coefficient

Rights: Copyright © 2010 Institute of Mathematical Statistics

Vol.38 • No. 3 • June 2010
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