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

Jianqing Fan, Yunbei Ma, Wei Dai

Research output: Contribution to journalArticle

97 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)1270-1284
Number of pages15
JournalJournal of the American Statistical Association
Volume109
Issue number507
DOIs
StatePublished - Sep 2014

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Conditional permutation
  • False positive rates
  • Sparsity
  • Sure independence screening
  • Variable selection

Fingerprint Dive into the research topics of 'Nonparametric Independence Screening in Sparse Ultra-High-Dimensional Varying Coefficient Models'. Together they form a unique fingerprint.

  • Cite this