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 Wei, F., J. Huang, and H. Li. 2011. Variable selection and estimation in high-dimensional varying-coefficient models. Statistica Sinica 21 (4):1515–40. doi:10.5705/ss.2009.316.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]).

摘要

本文重点介绍在协变量数量大于样本量的情况下，变系数模型的变量选择。将 B 样条基函数近似与改进的自适应组套索相结合，我们建立了选择一致性、收敛速度和渐近正态性。我们的贡献是边际非参数估计被用作自适应组套索的权重。仿真研究和两个实际数据应用表明，我们的方法比 Wei、Huang 和 Li ( 2011 ) 的方法表现更好 Wei、F.、J. Huang和H. Li。2011 年。高维变系数模型中的变量选择和估计。统计学21 (4): 1515 – 40。doi: 10.5705/ss.2009.316。[Crossref]、[PubMed]、[Web of Science®]、 [Google Scholar]）。