Modified adaptive group lasso for high-dimensional varying coefficient models

Abstract

This article focuses on variable selection for varying coefficient models in the case of the number of covariates being larger than the sample size. Combining B-spline basis function approximations with the modified adaptive group lasso, we establish selection consistency, convergence rate and asymptotic normality. Our contribution is that the marginal nonparametric estimates are used as weights of the adaptive group lasso. Simulation studies and two real data applications show that our method performs better than the method of Wei, Huang, and Li (2011).

Keywords:

• Marginal least squares estimates
• Selection consistency
• Varying coefficient models

Acknowledgments

The authors would like to thank the Editor and referees for their comments and valuable suggestions.

Additional information

Funding

Mingqiu Wang’s research was supported by the National Natural Science Foundation of China (11771250), the Natural Science Foundation of Shandong Province (ZR2019MA002). Xiaoning Kang’s research was fully supported by Ministry of Education of China (20YJC910007). Guo-Liang Tian’s research was fully supported by the National Natural Science Foundation of China (11771199)