On the sure screening properties of iteratively sure independence screening algorithms

Ning Zhang*, Wenxin Jiang, Yuting Lan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Fan and Lv (2008) proposed the path-breaking theory of sure independence screening (SIS) and an iterative algorithm (ISIS) to effectively reduce the predictor dimension for further variable selection approaches. Fan et al. (2009) extended ISIS to generalized linear models and introduced the Vanilla ISIS (Van-ISIS) algorithm, allowing selected predictors to be screened out in upcoming iterations. The success of SIS depends on its sure screening property, which was obtained by Fan and Lv (2008) under the marginal correlation assumption. However, despite wide applications of ISIS and Van-ISIS in various scientific fields, their sure screening properties have not been proved during the past decade. To fill this gap, we prove the sure screening properties of three different types of iterative algorithms for linear models without relying on the marginal correlation assumption, where ISIS and Van-ISIS can be regarded as two special cases of them.

Original languageEnglish (US)
JournalUnknown Journal
StatePublished - Dec 4 2018

Keywords

  • Iteratively sure independence screening
  • Penalized least squares
  • Sure screening property
  • Variable screening
  • Variable selection

ASJC Scopus subject areas

  • General

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