The Annals of Statistics

Consistent covariate selection and post model selection inference in semiparametric regression

Florentina Bunea

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Abstract

This paper presents a model selection technique of estimation in semiparametric regression models of the type $Y_{i}={\beta}^{\prime}\underbar{X}_{i}+f(T_{i})+W_{i}$ , 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.

Article information

Source
Ann. Statist., Volume 32, Number 3 (2004), 898-927.

Dates
First available in Project Euclid: 24 May 2004

Permanent link to this document
https://projecteuclid.org/euclid.aos/1085408490

Digital Object Identifier
doi:10.1214/009053604000000247

Mathematical Reviews number (MathSciNet)
MR2065193

Zentralblatt MATH identifier
1092.62045

Subjects
Primary: 62G05: Estimation 62F99: None of the above, but in this section
Secondary: 62G08: Nonparametric regression 62J02: General nonlinear regression

Keywords
Semiparametric regression consistent covariate selection post model selection inference penalized least squares oracle inequalities

Citation

Bunea, Florentina. Consistent covariate selection and post model selection inference in semiparametric regression. Ann. Statist. 32 (2004), no. 3, 898--927. doi:10.1214/009053604000000247. https://projecteuclid.org/euclid.aos/1085408490


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