TY - JOUR
T1 - Sequential profile Lasso for ultra-high-dimensional partially linear models
AU - Li, Yujie
AU - Li, Gaorong
AU - Tong, Tiejun
N1 - Funding Information:
Gaorong Li’s research was supported in part by the National Natural Science Foundation of China [number 11471029]. Tiejun Tong’s research was supported in part by the National Natural Science Foundation of China [number 11671338] and the Hong Kong Baptist University grants [grant number FRG2/15-16/019], [grant number FRG1/16-17/018].
PY - 2017/7/3
Y1 - 2017/7/3
N2 - In this paper, we study ultra-high-dimensional partially linear models when the dimension of the linear predictors grows exponentially with the sample size. For the variable screening, we propose a sequential profile Lasso method (SPLasso) and show that it possesses the screening property. SPLasso can also detect all relevant predictors with probability tending to one, no matter whether the ultra-high models involve both parametric and nonparametric parts. To select the best subset among the models generated by SPLasso, we propose an extended Bayesian information criterion (EBIC) for choosing the final model. We also conduct simulation studies and apply a real data example to assess the performance of the proposed method and compare with the existing method.
AB - In this paper, we study ultra-high-dimensional partially linear models when the dimension of the linear predictors grows exponentially with the sample size. For the variable screening, we propose a sequential profile Lasso method (SPLasso) and show that it possesses the screening property. SPLasso can also detect all relevant predictors with probability tending to one, no matter whether the ultra-high models involve both parametric and nonparametric parts. To select the best subset among the models generated by SPLasso, we propose an extended Bayesian information criterion (EBIC) for choosing the final model. We also conduct simulation studies and apply a real data example to assess the performance of the proposed method and compare with the existing method.
KW - extended Bayesian information criterion
KW - partially linear model
KW - screening property
KW - Sequential profile Lasso
KW - ultra-high-dimensional data
UR - http://www.scopus.com/inward/record.url?scp=85047118461&partnerID=8YFLogxK
U2 - 10.1080/24754269.2017.1396432
DO - 10.1080/24754269.2017.1396432
M3 - Journal article
AN - SCOPUS:85047118461
SN - 2475-4269
VL - 1
SP - 234
EP - 245
JO - Statistical Theory and Related Fields
JF - Statistical Theory and Related Fields
IS - 2
ER -