TY - JOUR
T1 - Nonparametric Independence Screening in Sparse Ultra-High-Dimensional Varying Coefficient Models
AU - Fan, Jianqing
AU - Ma, Yunbei
AU - Dai, Wei
N1 - Funding Information:
Jianqing Fan (E-mail: jqfan@princeton.edu) is Director, Center for Statistical Research, Academy of Mathematics and Systems Science, The Chinese Academy of Sciences, Beijing 100080, China, and the current Frederick L. Moore ’18 Professor of Finance, Professor of Statistics, and Chairman; and Wei Dai (E-mail: weidai@princeton.edu) is graduate student, Department of Operations Research and Financial Engineering, Princeton University, Princeton, NJ 08544. Yunbei Ma is Assistant Professor, School of Statistics, Southwestern University of Finance and Economics, Chengdu, Sichuan 611130, China (E-mail: myb@swufe.edu.cn). Fan was supported by National Institutes of Health grants R01-GM072611 and R01-GM100474, and National Science Foundation grant DMS-1206464, and Ma was supported by National Natural Science Foundation of China (grant no. 11301424). The authors thank the editor, the associate editor, and referees for their constructive comments.
Publisher Copyright:
© 2014 American Statistical Association.
PY - 2014/9
Y1 - 2014/9
N2 - The varying coefficient model is an important class of nonparametric statistical model, which allows us to examine how the effects of covariates vary with exposure variables. When the number of covariates is large, the issue of variable selection arises. In this article, we propose and investigate marginal nonparametric screening methods to screen variables in sparse ultra-high-dimensional varying coefficient models. The proposed nonparametric independence screening (NIS) selects variables by ranking a measure of the nonparametric marginal contributions of each covariate given the exposure variable. The sure independent screening property is established under some mild technical conditions when the dimensionality is of nonpolynomial order, and the dimensionality reduction of NIS is quantified. To enhance the practical utility and finite sample performance, two data-driven iterative NIS (INIS) methods are proposed for selecting thresholding parameters and variables: conditional permutation and greedy methods, resulting in conditional-INIS and greedy-INIS. The effectiveness and flexibility of the proposed methods are further illustrated by simulation studies and real data applications.
AB - The varying coefficient model is an important class of nonparametric statistical model, which allows us to examine how the effects of covariates vary with exposure variables. When the number of covariates is large, the issue of variable selection arises. In this article, we propose and investigate marginal nonparametric screening methods to screen variables in sparse ultra-high-dimensional varying coefficient models. The proposed nonparametric independence screening (NIS) selects variables by ranking a measure of the nonparametric marginal contributions of each covariate given the exposure variable. The sure independent screening property is established under some mild technical conditions when the dimensionality is of nonpolynomial order, and the dimensionality reduction of NIS is quantified. To enhance the practical utility and finite sample performance, two data-driven iterative NIS (INIS) methods are proposed for selecting thresholding parameters and variables: conditional permutation and greedy methods, resulting in conditional-INIS and greedy-INIS. The effectiveness and flexibility of the proposed methods are further illustrated by simulation studies and real data applications.
KW - Conditional permutation
KW - False positive rates
KW - Sparsity
KW - Sure independence screening
KW - Variable selection
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U2 - 10.1080/01621459.2013.879828
DO - 10.1080/01621459.2013.879828
M3 - Article
C2 - 25309009
AN - SCOPUS:84907494426
SN - 0162-1459
VL - 109
SP - 1270
EP - 1284
JO - Journal of the American Statistical Association
JF - Journal of the American Statistical Association
IS - 507
ER -