Nonconcave penalized estimation for partially linear models with longitudinal data

Abstract

A nonconcave penalized estimation method is proposed for partially linear models with longitudinal data when the number of parameters diverges with the sample size. The proposed procedure can simultaneously estimate the parameters and select the important variables. Under some regularity conditions, the rate of convergence and asymptotic normality of the resulting estimators are established. In addition, an iterative algorithm is proposed to implement the proposed estimators. To improve efficiency for regression coefficients, the estimation of the covariance function is integrated in the iterative algorithm. Simulation studies are carried out to demonstrate that the proposed method performs well, and a real data example is analysed to illustrate the proposed procedure.

Keywords:

• partially linear model
• longitudinal data
• variable selection
• smoothing clipped absolute deviation

AMS Subject Classifications:

• Primary: 62G05
• Secondary: 62G20

Acknowledgements

The authors are grateful to the editors and the referees for thoughtful comments and suggestions, which helped improve the paper substantially.

Disclosure statement

No potential conflict of interest was reported by the authors.

Funding

Yiping Yang's research was supported by the National Natural Science Foundation of China [grant number 11301569]. Gaorong Li's research was supported by the National Natural Science Foundation of China [grant number 11471029], [grant number 11472057], the Beijing Natural Science Foundation [grant number 1142002], the Science and Technology Project of Beijing Municipal Education Commission [grant number KM201410005010] and Program for JingHua Talents in Beijing University of Technology [grant number 2013-JH-L07].