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June 2004 Consistent covariate selection and post model selection inference in semiparametric regression
Florentina Bunea
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Ann. Statist. 32(3): 898-927 (June 2004). DOI: 10.1214/009053604000000247


This paper presents a model selection technique of estimation in semiparametric regression models of the type $Y_{i}={\beta}^{\prime}\underline{X}_{i}+f(T_{i})+W_{i}$ , i=1,…,n. The parametric and nonparametric components are estimated simultaneously by this procedure. Estimation is based on a collection of finite-dimensional models, using a penalized least squares criterion for selection. We show that by tailoring the penalty terms developed for nonparametric regression to semiparametric models, we can consistently estimate the subset of nonzero coefficients of the linear part. Moreover, the selected estimator of the linear component is asymptotically normal.


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Florentina Bunea. "Consistent covariate selection and post model selection inference in semiparametric regression." Ann. Statist. 32 (3) 898 - 927, June 2004.


Published: June 2004
First available in Project Euclid: 24 May 2004

zbMATH: 1092.62045
MathSciNet: MR2065193
Digital Object Identifier: 10.1214/009053604000000247

Primary: 62F99 , 62G05
Secondary: 62G08 , 62J02

Keywords: consistent covariate selection , Oracle inequalities , penalized least squares , post model selection inference , semiparametric regression

Rights: Copyright © 2004 Institute of Mathematical Statistics


Vol.32 • No. 3 • June 2004
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