Nonparametric Independence Screening in Sparse Ultra-High-Dimensional Varying Coefficient Models

• 成果类型: Article
• 署名作者: Fan, Jianqing; Ma, Yunbei; Dai, Wei
• 署名单位: Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Princeton University; Southwestern University of Finance & Economics - China
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2013.879828
• 发表日期: 2014
• 页码: 1270-1284
• 关键词: nonconcave penalized likelihood; variable selection; regularization

摘要

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.