TY - JOUR
T1 - Profile forward regression screening for ultra-high dimensional semiparametric varying coefficient partially linear models
AU - Li, Yujie
AU - Li, Gaorong
AU - Lian, Heng
AU - Tong, Tiejun
N1 - Funding Information:
Gaorong Li's research was supported by the National Natural Science Foundation of China (Grant No. 11471029), the Beijing Natural Science Foundation (Grant No. 1142002) and the Science and Technology Project of Beijing Municipal Education Commission (Grant No. KM201410005010). Tiejun Tong's research was supported by the Hong Kong Baptist University FRG grants FRG1/14-15/044, FRG2/15-16/019 and FRG2/15-16/038, and the National Natural Science Foundation of China (Grant No. 11671338). The authors would like to thank the Editor-in-Chief, Christian Genest, an Associate Editor, and two referees for their helpful comments that helped to improve an earlier version of this article.
PY - 2017/3/1
Y1 - 2017/3/1
N2 - In this paper, we consider semiparametric varying coefficient partially linear models when the predictor variables of the linear part are ultra-high dimensional where the dimensionality grows exponentially with the sample size. We propose a profile forward regression (PFR) method to perform variable screening for ultra-high dimensional linear predictor variables. The proposed PFR algorithm can not only identify all relevant predictors consistently even for ultra-high semiparametric models including both nonparametric and parametric parts, but also possesses the screening consistency property. To determine whether or not to include the candidate predictor in the model of selected ones, we adopt an extended Bayesian information criterion (EBIC) to select the “best” candidate model. Simulation studies and a real data example are also carried out to assess the performance of the proposed method and to compare it with existing screening methods.
AB - In this paper, we consider semiparametric varying coefficient partially linear models when the predictor variables of the linear part are ultra-high dimensional where the dimensionality grows exponentially with the sample size. We propose a profile forward regression (PFR) method to perform variable screening for ultra-high dimensional linear predictor variables. The proposed PFR algorithm can not only identify all relevant predictors consistently even for ultra-high semiparametric models including both nonparametric and parametric parts, but also possesses the screening consistency property. To determine whether or not to include the candidate predictor in the model of selected ones, we adopt an extended Bayesian information criterion (EBIC) to select the “best” candidate model. Simulation studies and a real data example are also carried out to assess the performance of the proposed method and to compare it with existing screening methods.
KW - EBIC
KW - Profile forward regression
KW - Screening consistency property
KW - Ultra-high dimension
KW - Variable screening
KW - Varying coefficient partially linear model
UR - http://www.scopus.com/inward/record.url?scp=85008608200&partnerID=8YFLogxK
U2 - 10.1016/j.jmva.2016.12.006
DO - 10.1016/j.jmva.2016.12.006
M3 - Journal article
AN - SCOPUS:85008608200
SN - 0047-259X
VL - 155
SP - 133
EP - 150
JO - Journal of Multivariate Analysis
JF - Journal of Multivariate Analysis
ER -