Variable Selection in Semiparametric Regression Modeling.

Annals of Statistics
Runze Li, Hua Liang

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 select significant variables for parametric portion. Thus, it is much more challenging than that for parametric models such as linear models and generalized linear models because traditional variable selection procedures including stepwise regression and the best subset selection require model selection to nonparametric components for each submodel. This leads to very heavy computational burden. In this paper, we propose a class of variable selection procedures for semiparametric regression models using nonconcave penalized likelihood. The newly proposed procedures are distinguished from the traditional ones in that they delete insignificant variables and estimate the coefficients of significant variables simultaneously. This allows us to establish the sampling properties of the resulting estimate. We first establish the rate of convergence of the resulting estimate. With proper choices of penalty functions and regularization parameters, we then establish the asymptotic normality of the resulting e...Continue Reading

References

Jan 6, 2009·Annals of Statistics·Runze Li, Hua Liang
Jan 1, 2005·Annals of Statistics·David R Hunter, Runze Li

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Citations

Nov 27, 2008·Lifetime Data Analysis·Xingwei TongJianguo Sun
Jun 12, 2012·Journal of Nonparametric Statistics·Ying Dai, Shuangge Ma
Aug 3, 2010·Journal of the American Statistical Association·Yiyun ZhangChih-Ling Tsai
Aug 7, 2010·Journal of the American Statistical Association·Yehua LiRaymond J Carroll
Nov 29, 2011·Journal of the American Statistical Association·Hao Helen ZhangYufeng Liu
Apr 18, 2012·Biometrics·Jun Yan, Jian Huang
Feb 1, 2009·Annals of the Institute of Statistical Mathematics·Grace Y YiHua Liang
Mar 29, 2014·Journal of the American Statistical Association·Jingyuan LiuRongling Wu
Jan 1, 2013·Journal of Computational and Graphical Statistics : a Joint Publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America·Bingqing LinJiming Jiang
Jan 1, 2017·Communications in Statistics: Theory and Methods·Guangren YangXia Cui
Jan 6, 2009·Annals of Statistics·Runze Li, Hua Liang
Jan 29, 2009·Annals of Statistics·Clifford Lam, Jiangqing Fan
Aug 1, 2008·Annals of Statistics·Hui Zou, Runze Li
Nov 26, 2010·Annals of Statistics·Wenyang ZhangYan Sun
Apr 22, 2017·Annals of Statistics·Tianqi ZhaoHan Liu
Mar 9, 2010·Bernoulli : Official Journal of the Bernoulli Society for Mathematical Statistics and Probability·Yanyuan Ma, Runze Li
Jan 1, 2012·Electronic Journal of Statistics·Yanyuan Ma, Yuanjia Wang

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