The Annals of Statistics

Variable selection in semiparametric regression modeling

Runze Li and Hua Liang

Full-text: Open access

Abstract

In this paper, we are concerned with how to select significant variables in semiparametric modeling. Variable selection for semiparametric regression models consists of two components: model selection for nonparametric components and selection of significant variables for the parametric portion. Thus, semiparametric variable selection is much more challenging than parametric variable selection (e.g., linear and generalized linear models) because traditional variable selection procedures including stepwise regression and the best subset selection now require separate model selection for the nonparametric components for each submodel. This leads to a very heavy computational burden. In this paper, we propose a class of variable selection procedures for semiparametric regression models using nonconcave penalized likelihood. We establish the rate of convergence of the resulting estimate. With proper choices of penalty functions and regularization parameters, we show the asymptotic normality of the resulting estimate and further demonstrate that the proposed procedures perform as well as an oracle procedure. A semiparametric generalized likelihood ratio test is proposed to select significant variables in the nonparametric component. We investigate the asymptotic behavior of the proposed test and demonstrate that its limiting null distribution follows a chi-square distribution which is independent of the nuisance parameters. Extensive Monte Carlo simulation studies are conducted to examine the finite sample performance of the proposed variable selection procedures.

Article information

Source
Ann. Statist., Volume 36, Number 1 (2008), 261-286.

Dates
First available in Project Euclid: 1 February 2008

Permanent link to this document
https://projecteuclid.org/euclid.aos/1201877301

Digital Object Identifier
doi:10.1214/009053607000000604

Mathematical Reviews number (MathSciNet)
MR2387971

Zentralblatt MATH identifier
1132.62027

Subjects
Primary: 62G08: Nonparametric regression 62G10: Hypothesis testing
Secondary: 62G20: Asymptotic properties

Keywords
Local linear regression nonconcave penalized likelihood SCAD varying coefficient models

Citation

Li, Runze; Liang, Hua. Variable selection in semiparametric regression modeling. Ann. Statist. 36 (2008), no. 1, 261--286. doi:10.1214/009053607000000604. https://projecteuclid.org/euclid.aos/1201877301


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