Nonparametric independence screening in sparse ultra-high-dimensional additive models

Jianqing Fan, Yang Feng, Rui Song

Research output: Contribution to journalArticle

250 Scopus citations

Abstract

A variable screening procedure via correlation learning was proposed by Fan and Lv (2008) to reduce dimensionality in sparse ultra-highdimensional models. Even when the true model is linear, the marginal regression can be highly nonlinear. To address this issue, we further extend the correlation learning to marginal nonparametric learning. Our nonparametric independence screening (NIS) is a specific type of sure independence screening. We propose several closely related variable screening procedures. We show that with general nonparametric models, under some mild technical conditions, the proposed independence screening methods have a sure screening property. The extentto which the dimensionality can be reduced by independence screening is also explicitly quantified. As a methodological extension, we also propose a data-driven thresholding and an iterative nonparametric independence screening (INIS) method to enhance the finite- sample performance for fitting sparse additive models. The simulation results and a real data analysis demonstrate that the proposed procedure works well with moderate sample size and large dimension and performs better than competing methods.

Original languageEnglish (US)
Pages (from-to)544-557
Number of pages14
JournalJournal of the American Statistical Association
Volume106
Issue number494
DOIs
StatePublished - Jun 2011

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Additive model
  • Independent learning
  • Nonparametric independence screening
  • Nonparametric regression
  • Sparsity
  • Sure independence screening
  • Variable selection

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